Leonardo

Thinking Machines: A Layman's Introduction to Logic, Boolean Algebra, and Computers byIrving AdlerReview by: James GipsLeonardo, Vol. 10, No. 2 (Spring, 1977), p. 158Published by: The MIT PressStable URL: http://www.jstor.org/stable/1573706 .

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effect of accidental gene recombinations in germ cells, but also the impact on the inherited structures of unique sensory histories' (p. 219). In a sense probably not meant by the author, the last phrase could mean that there is feedback from sensory experience to the gene.

Geneticists claim that these innate deep structures are the outcome of selection. Yet some of them have little survival value; they do not contribute to homeostasis. Another point is that humans have not existed long enough for the selection process to have achieved such universality over such a wide population. The brain sciences appear to be establishing the view that human cultural progress has been accelerated by feedback to the genes during ontogenetic development. This is one example of the kind of fundamental question raised by the book. It incorporates much of the most recent brain research, though some, like the work of Colin Blakemore at Cambridge (U.K.), is not acknowledged.

The Language of Mathematics. Frank Land. John Murray, London, 1975, 264 pp., illus. Paper, ?1.25. Reviewed by G. Stanley Smith*

This large-format paperback is a re-issue of the book originally published in 1960. Since there have been several reprints, one can infer that its popularity has been well established. Attractively presented with numerous two-colour drawings, it is a real bargain- made possible, as appears from a remark in the preface, through the co-operation of the Shell International Petroleum Company.

Its main purpose is to stimulate those who may have considered mathematics a distasteful and unnecessary study to explore the subject and perhaps to experience some unexpected delights. They will find in the book that even the most elementary operations in arithmetic, algebra and geometry are explained with great clarity and with apt illustrations. As a bonus, many odd bits of information will be collected on the way, such as the fact that the average silkworm produces 450 metres of thread (introduced to explain the derivation of the denier unit for silk or nylon thread). In a useful section on statistics, one is gently led through the ideas of distributions, histograms and standard deviation to correlation, significance tests, ways of studying reliability and validity of results and methods of assessing probability. At the end one should be in a better position to understand the special terms of statistical inference that permeate various branches of knowledge.

Historical background is prominent, particularly in the sections on number systems and how they have developed, units of length, weight, capacity and money, and time and the calendar. New units, including those for money in Britain, are not introduced, so certain calculations involving money at various places in the book have an out-of-date appearance.

Readers who are not altogether ignorant of mathematics will skip large portions of the text, but they are likely to be forced to a halt when, for instance, the author brings together the number of teams in the last five rounds of the British Football Association Cup, the successive frequencies of the C notes on a piano, and the profile of organ pipes to illumine exponential curves.

With all the wealth of illustrative diagrams and clear expositions, an artist feeling in need of some mathematical bases for his work will find considerable help, particularly in the sections on geometry, topology and the golden section. The chapter on the Fibonacci sequence and the golden section is one of the best short treatments of the subject that I have read.

It seems a pity, however, that, after 15 years, the author has not taken the opportunity to reflect some of the more recent changes in the presentation of mathematics by teachers in relation to the theory of sets and groups (somewhat inadequately represented here in two or three pages), matrices (not even referred to) and general structural ideas in algebra. But, I suppose, one cannot have everything in this very enjoyable book.

Thinking Machines: A Layman's Introduction to Logic, Boolean

effect of accidental gene recombinations in germ cells, but also the impact on the inherited structures of unique sensory histories' (p. 219). In a sense probably not meant by the author, the last phrase could mean that there is feedback from sensory experience to the gene.

Geneticists claim that these innate deep structures are the outcome of selection. Yet some of them have little survival value; they do not contribute to homeostasis. Another point is that humans have not existed long enough for the selection process to have achieved such universality over such a wide population. The brain sciences appear to be establishing the view that human cultural progress has been accelerated by feedback to the genes during ontogenetic development. This is one example of the kind of fundamental question raised by the book. It incorporates much of the most recent brain research, though some, like the work of Colin Blakemore at Cambridge (U.K.), is not acknowledged.

The Language of Mathematics. Frank Land. John Murray, London, 1975, 264 pp., illus. Paper, ?1.25. Reviewed by G. Stanley Smith*

This large-format paperback is a re-issue of the book originally published in 1960. Since there have been several reprints, one can infer that its popularity has been well established. Attractively presented with numerous two-colour drawings, it is a real bargain- made possible, as appears from a remark in the preface, through the co-operation of the Shell International Petroleum Company.

Its main purpose is to stimulate those who may have considered mathematics a distasteful and unnecessary study to explore the subject and perhaps to experience some unexpected delights. They will find in the book that even the most elementary operations in arithmetic, algebra and geometry are explained with great clarity and with apt illustrations. As a bonus, many odd bits of information will be collected on the way, such as the fact that the average silkworm produces 450 metres of thread (introduced to explain the derivation of the denier unit for silk or nylon thread). In a useful section on statistics, one is gently led through the ideas of distributions, histograms and standard deviation to correlation, significance tests, ways of studying reliability and validity of results and methods of assessing probability. At the end one should be in a better position to understand the special terms of statistical inference that permeate various branches of knowledge.

Historical background is prominent, particularly in the sections on number systems and how they have developed, units of length, weight, capacity and money, and time and the calendar. New units, including those for money in Britain, are not introduced, so certain calculations involving money at various places in the book have an out-of-date appearance.

Readers who are not altogether ignorant of mathematics will skip large portions of the text, but they are likely to be forced to a halt when, for instance, the author brings together the number of teams in the last five rounds of the British Football Association Cup, the successive frequencies of the C notes on a piano, and the profile of organ pipes to illumine exponential curves.

With all the wealth of illustrative diagrams and clear expositions, an artist feeling in need of some mathematical bases for his work will find considerable help, particularly in the sections on geometry, topology and the golden section. The chapter on the Fibonacci sequence and the golden section is one of the best short treatments of the subject that I have read.

It seems a pity, however, that, after 15 years, the author has not taken the opportunity to reflect some of the more recent changes in the presentation of mathematics by teachers in relation to the theory of sets and groups (somewhat inadequately represented here in two or three pages), matrices (not even referred to) and general structural ideas in algebra. But, I suppose, one cannot have everything in this very enjoyable book.

Thinking Machines: A Layman's Introduction to Logic, Boolean

effect of accidental gene recombinations in germ cells, but also the impact on the inherited structures of unique sensory histories' (p. 219). In a sense probably not meant by the author, the last phrase could mean that there is feedback from sensory experience to the gene.

Geneticists claim that these innate deep structures are the outcome of selection. Yet some of them have little survival value; they do not contribute to homeostasis. Another point is that humans have not existed long enough for the selection process to have achieved such universality over such a wide population. The brain sciences appear to be establishing the view that human cultural progress has been accelerated by feedback to the genes during ontogenetic development. This is one example of the kind of fundamental question raised by the book. It incorporates much of the most recent brain research, though some, like the work of Colin Blakemore at Cambridge (U.K.), is not acknowledged.

The Language of Mathematics. Frank Land. John Murray, London, 1975, 264 pp., illus. Paper, ?1.25. Reviewed by G. Stanley Smith*

This large-format paperback is a re-issue of the book originally published in 1960. Since there have been several reprints, one can infer that its popularity has been well established. Attractively presented with numerous two-colour drawings, it is a real bargain- made possible, as appears from a remark in the preface, through the co-operation of the Shell International Petroleum Company.

Its main purpose is to stimulate those who may have considered mathematics a distasteful and unnecessary study to explore the subject and perhaps to experience some unexpected delights. They will find in the book that even the most elementary operations in arithmetic, algebra and geometry are explained with great clarity and with apt illustrations. As a bonus, many odd bits of information will be collected on the way, such as the fact that the average silkworm produces 450 metres of thread (introduced to explain the derivation of the denier unit for silk or nylon thread). In a useful section on statistics, one is gently led through the ideas of distributions, histograms and standard deviation to correlation, significance tests, ways of studying reliability and validity of results and methods of assessing probability. At the end one should be in a better position to understand the special terms of statistical inference that permeate various branches of knowledge.

Historical background is prominent, particularly in the sections on number systems and how they have developed, units of length, weight, capacity and money, and time and the calendar. New units, including those for money in Britain, are not introduced, so certain calculations involving money at various places in the book have an out-of-date appearance.

Readers who are not altogether ignorant of mathematics will skip large portions of the text, but they are likely to be forced to a halt when, for instance, the author brings together the number of teams in the last five rounds of the British Football Association Cup, the successive frequencies of the C notes on a piano, and the profile of organ pipes to illumine exponential curves.

With all the wealth of illustrative diagrams and clear expositions, an artist feeling in need of some mathematical bases for his work will find considerable help, particularly in the sections on geometry, topology and the golden section. The chapter on the Fibonacci sequence and the golden section is one of the best short treatments of the subject that I have read.

It seems a pity, however, that, after 15 years, the author has not taken the opportunity to reflect some of the more recent changes in the presentation of mathematics by teachers in relation to the theory of sets and groups (somewhat inadequately represented here in two or three pages), matrices (not even referred to) and general structural ideas in algebra. But, I suppose, one cannot have everything in this very enjoyable book.

Thinking Machines: A Layman's Introduction to Logic, Boolean

effect of accidental gene recombinations in germ cells, but also the impact on the inherited structures of unique sensory histories' (p. 219). In a sense probably not meant by the author, the last phrase could mean that there is feedback from sensory experience to the gene.

Geneticists claim that these innate deep structures are the outcome of selection. Yet some of them have little survival value; they do not contribute to homeostasis. Another point is that humans have not existed long enough for the selection process to have achieved such universality over such a wide population. The brain sciences appear to be establishing the view that human cultural progress has been accelerated by feedback to the genes during ontogenetic development. This is one example of the kind of fundamental question raised by the book. It incorporates much of the most recent brain research, though some, like the work of Colin Blakemore at Cambridge (U.K.), is not acknowledged.

The Language of Mathematics. Frank Land. John Murray, London, 1975, 264 pp., illus. Paper, ?1.25. Reviewed by G. Stanley Smith*

This large-format paperback is a re-issue of the book originally published in 1960. Since there have been several reprints, one can infer that its popularity has been well established. Attractively presented with numerous two-colour drawings, it is a real bargain- made possible, as appears from a remark in the preface, through the co-operation of the Shell International Petroleum Company.

Its main purpose is to stimulate those who may have considered mathematics a distasteful and unnecessary study to explore the subject and perhaps to experience some unexpected delights. They will find in the book that even the most elementary operations in arithmetic, algebra and geometry are explained with great clarity and with apt illustrations. As a bonus, many odd bits of information will be collected on the way, such as the fact that the average silkworm produces 450 metres of thread (introduced to explain the derivation of the denier unit for silk or nylon thread). In a useful section on statistics, one is gently led through the ideas of distributions, histograms and standard deviation to correlation, significance tests, ways of studying reliability and validity of results and methods of assessing probability. At the end one should be in a better position to understand the special terms of statistical inference that permeate various branches of knowledge.

Historical background is prominent, particularly in the sections on number systems and how they have developed, units of length, weight, capacity and money, and time and the calendar. New units, including those for money in Britain, are not introduced, so certain calculations involving money at various places in the book have an out-of-date appearance.

Readers who are not altogether ignorant of mathematics will skip large portions of the text, but they are likely to be forced to a halt when, for instance, the author brings together the number of teams in the last five rounds of the British Football Association Cup, the successive frequencies of the C notes on a piano, and the profile of organ pipes to illumine exponential curves.

With all the wealth of illustrative diagrams and clear expositions, an artist feeling in need of some mathematical bases for his work will find considerable help, particularly in the sections on geometry, topology and the golden section. The chapter on the Fibonacci sequence and the golden section is one of the best short treatments of the subject that I have read.

It seems a pity, however, that, after 15 years, the author has not taken the opportunity to reflect some of the more recent changes in the presentation of mathematics by teachers in relation to the theory of sets and groups (somewhat inadequately represented here in two or three pages), matrices (not even referred to) and general structural ideas in algebra. But, I suppose, one cannot have everything in this very enjoyable book.

Thinking Machines: A Layman's Introduction to Logic, Boolean Algebra, and Computers. Revised and enlarged edition. Irving. Adler. John Day, New York, 1974. Reviewed by James Gips** Algebra, and Computers. Revised and enlarged edition. Irving. Adler. John Day, New York, 1974. Reviewed by James Gips** Algebra, and Computers. Revised and enlarged edition. Irving. Adler. John Day, New York, 1974. Reviewed by James Gips** Algebra, and Computers. Revised and enlarged edition. Irving. Adler. John Day, New York, 1974. Reviewed by James Gips**

*3 Marine Drive, Seaford, Sussex, England. *3 Marine Drive, Seaford, Sussex, England. *3 Marine Drive, Seaford, Sussex, England. *3 Marine Drive, Seaford, Sussex, England.

Adler begins his book with a brief discussion of some of the tasks performed by computers-calculating payrolls, guiding missiles, playing checkers and chess, composing music. He then attempts to describe for the layman how computers work. However, as in so many other introductory descriptions of computers, computers are described predominantly at the logic-circuit level. The bulk of this book is concerned with Boolean algebra and propositional logic (the theory behind logic circuits), with AND, OR and NOT gates (the basic components of logic circuits) and with how AND, OR and NOT gates can be combined into logic circuits used in computers (for example, circuits that add two numbers).

The reader is confronted with the problem described by H. A. Simon: 'In [complex] systems the whole is more than the sum of its parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in- principle reductionist may be at the same time a pragmatic holist.' [H. A. Simon, The Sciences of the Artificial (Cambridge, Mass.: M.I.T. Press, 1969) p. 86.] Thus, it is possible to have a basic understanding of how computers work at the logic-circuit level yet have only the haziest idea of how computers work at the higher levels (i.e. levels of components, machine languages and programming languages).

The description of Boolean algebra and logic circuits is well done in this book. There are also descriptions of computers at the higher levels, but they are all too brief and sometimes outdated. There is no description of computers at the highest level, at the equivalent of the chess-strategy level. Yet, I believe that this is the critical level for understanding computers. What an introductory book about computers for laymen would convey most profitably is a feeling about how one converts knowledge about a process- be it calculating payrolls, guiding missiles, playing games or composing music-into an algorithm, into a list of instructions a computer can follow. The mechanics and theory of how computers follow instructions are of as little concern to a layman as are the intricacies of a carburetor to a fledgling automobile driver.

In summary, if one wants to gain an understanding of Boolean algebra and its use in computer logic circuits, this is a good book to study. If one wants to gain a general understanding of 'thinking machines', this is not the right book. The subtitle of this book should be its title.

On the Rationalization of Sight. William M. Ivins, Jr. Da Capo, New York, 1973. 44 pp. + 2 annexes, illus. $18.00. Reviewed by F. H. C. Marriott:

For the late William M. Ivins, Jr., the discovery of the laws of perspective was the most important event of the Renaissance. With the development of engraving, it made possible the use of technical illustrations giving visual information in an unambiguous way. Who made the discovery is unknown, but it is clear that what was discovered was a set of rules for the guidance of artists, rather than mathematical theorems. In this sense, perspective antedated projective geometry.

The first known description of the 'costruzione legittima' was by Alberti in 1435-6. In 1505, Jean Pelerin ('Viator') published his illustrated guide to perspective drawing, De Artificiali Perspectiva, giving a slightly different, but equivalent, construction. Ivins discusses how these rules were discovered and gives a most convincing exposition of the way in which a simple model could be used to demonstrate each of the two constructions.

Albrecht Durer also wrote on perspective, but his description (1525) is wrong. Further, curious distortions appear in his work; in particular, his 'great showpiece of perspective rendering', the print of St. Jerome in his study (1514), is grossly out of perspective, if the room and furniture are supposed to have their ordinary shapes. Is it possible he had not studied perspective

**Dept. of Biomathematics, University of California, Los

Adler begins his book with a brief discussion of some of the tasks performed by computers-calculating payrolls, guiding missiles, playing checkers and chess, composing music. He then attempts to describe for the layman how computers work. However, as in so many other introductory descriptions of computers, computers are described predominantly at the logic-circuit level. The bulk of this book is concerned with Boolean algebra and propositional logic (the theory behind logic circuits), with AND, OR and NOT gates (the basic components of logic circuits) and with how AND, OR and NOT gates can be combined into logic circuits used in computers (for example, circuits that add two numbers).

The reader is confronted with the problem described by H. A. Simon: 'In [complex] systems the whole is more than the sum of its parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in- principle reductionist may be at the same time a pragmatic holist.' [H. A. Simon, The Sciences of the Artificial (Cambridge, Mass.: M.I.T. Press, 1969) p. 86.] Thus, it is possible to have a basic understanding of how computers work at the logic-circuit level yet have only the haziest idea of how computers work at the higher levels (i.e. levels of components, machine languages and programming languages).

The description of Boolean algebra and logic circuits is well done in this book. There are also descriptions of computers at the higher levels, but they are all too brief and sometimes outdated. There is no description of computers at the highest level, at the equivalent of the chess-strategy level. Yet, I believe that this is the critical level for understanding computers. What an introductory book about computers for laymen would convey most profitably is a feeling about how one converts knowledge about a process- be it calculating payrolls, guiding missiles, playing games or composing music-into an algorithm, into a list of instructions a computer can follow. The mechanics and theory of how computers follow instructions are of as little concern to a layman as are the intricacies of a carburetor to a fledgling automobile driver.

In summary, if one wants to gain an understanding of Boolean algebra and its use in computer logic circuits, this is a good book to study. If one wants to gain a general understanding of 'thinking machines', this is not the right book. The subtitle of this book should be its title.

On the Rationalization of Sight. William M. Ivins, Jr. Da Capo, New York, 1973. 44 pp. + 2 annexes, illus. $18.00. Reviewed by F. H. C. Marriott:

For the late William M. Ivins, Jr., the discovery of the laws of perspective was the most important event of the Renaissance. With the development of engraving, it made possible the use of technical illustrations giving visual information in an unambiguous way. Who made the discovery is unknown, but it is clear that what was discovered was a set of rules for the guidance of artists, rather than mathematical theorems. In this sense, perspective antedated projective geometry.

The first known description of the 'costruzione legittima' was by Alberti in 1435-6. In 1505, Jean Pelerin ('Viator') published his illustrated guide to perspective drawing, De Artificiali Perspectiva, giving a slightly different, but equivalent, construction. Ivins discusses how these rules were discovered and gives a most convincing exposition of the way in which a simple model could be used to demonstrate each of the two constructions.

Albrecht Durer also wrote on perspective, but his description (1525) is wrong. Further, curious distortions appear in his work; in particular, his 'great showpiece of perspective rendering', the print of St. Jerome in his study (1514), is grossly out of perspective, if the room and furniture are supposed to have their ordinary shapes. Is it possible he had not studied perspective

**Dept. of Biomathematics, University of California, Los

Adler begins his book with a brief discussion of some of the tasks performed by computers-calculating payrolls, guiding missiles, playing checkers and chess, composing music. He then attempts to describe for the layman how computers work. However, as in so many other introductory descriptions of computers, computers are described predominantly at the logic-circuit level. The bulk of this book is concerned with Boolean algebra and propositional logic (the theory behind logic circuits), with AND, OR and NOT gates (the basic components of logic circuits) and with how AND, OR and NOT gates can be combined into logic circuits used in computers (for example, circuits that add two numbers).

The reader is confronted with the problem described by H. A. Simon: 'In [complex] systems the whole is more than the sum of its parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in- principle reductionist may be at the same time a pragmatic holist.' [H. A. Simon, The Sciences of the Artificial (Cambridge, Mass.: M.I.T. Press, 1969) p. 86.] Thus, it is possible to have a basic understanding of how computers work at the logic-circuit level yet have only the haziest idea of how computers work at the higher levels (i.e. levels of components, machine languages and programming languages).

The description of Boolean algebra and logic circuits is well done in this book. There are also descriptions of computers at the higher levels, but they are all too brief and sometimes outdated. There is no description of computers at the highest level, at the equivalent of the chess-strategy level. Yet, I believe that this is the critical level for understanding computers. What an introductory book about computers for laymen would convey most profitably is a feeling about how one converts knowledge about a process- be it calculating payrolls, guiding missiles, playing games or composing music-into an algorithm, into a list of instructions a computer can follow. The mechanics and theory of how computers follow instructions are of as little concern to a layman as are the intricacies of a carburetor to a fledgling automobile driver.

In summary, if one wants to gain an understanding of Boolean algebra and its use in computer logic circuits, this is a good book to study. If one wants to gain a general understanding of 'thinking machines', this is not the right book. The subtitle of this book should be its title.

On the Rationalization of Sight. William M. Ivins, Jr. Da Capo, New York, 1973. 44 pp. + 2 annexes, illus. $18.00. Reviewed by F. H. C. Marriott:

For the late William M. Ivins, Jr., the discovery of the laws of perspective was the most important event of the Renaissance. With the development of engraving, it made possible the use of technical illustrations giving visual information in an unambiguous way. Who made the discovery is unknown, but it is clear that what was discovered was a set of rules for the guidance of artists, rather than mathematical theorems. In this sense, perspective antedated projective geometry.

The first known description of the 'costruzione legittima' was by Alberti in 1435-6. In 1505, Jean Pelerin ('Viator') published his illustrated guide to perspective drawing, De Artificiali Perspectiva, giving a slightly different, but equivalent, construction. Ivins discusses how these rules were discovered and gives a most convincing exposition of the way in which a simple model could be used to demonstrate each of the two constructions.

Albrecht Durer also wrote on perspective, but his description (1525) is wrong. Further, curious distortions appear in his work; in particular, his 'great showpiece of perspective rendering', the print of St. Jerome in his study (1514), is grossly out of perspective, if the room and furniture are supposed to have their ordinary shapes. Is it possible he had not studied perspective

**Dept. of Biomathematics, University of California, Los

Adler begins his book with a brief discussion of some of the tasks performed by computers-calculating payrolls, guiding missiles, playing checkers and chess, composing music. He then attempts to describe for the layman how computers work. However, as in so many other introductory descriptions of computers, computers are described predominantly at the logic-circuit level. The bulk of this book is concerned with Boolean algebra and propositional logic (the theory behind logic circuits), with AND, OR and NOT gates (the basic components of logic circuits) and with how AND, OR and NOT gates can be combined into logic circuits used in computers (for example, circuits that add two numbers).

The reader is confronted with the problem described by H. A. Simon: 'In [complex] systems the whole is more than the sum of its parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in- principle reductionist may be at the same time a pragmatic holist.' [H. A. Simon, The Sciences of the Artificial (Cambridge, Mass.: M.I.T. Press, 1969) p. 86.] Thus, it is possible to have a basic understanding of how computers work at the logic-circuit level yet have only the haziest idea of how computers work at the higher levels (i.e. levels of components, machine languages and programming languages).

The description of Boolean algebra and logic circuits is well done in this book. There are also descriptions of computers at the higher levels, but they are all too brief and sometimes outdated. There is no description of computers at the highest level, at the equivalent of the chess-strategy level. Yet, I believe that this is the critical level for understanding computers. What an introductory book about computers for laymen would convey most profitably is a feeling about how one converts knowledge about a process- be it calculating payrolls, guiding missiles, playing games or composing music-into an algorithm, into a list of instructions a computer can follow. The mechanics and theory of how computers follow instructions are of as little concern to a layman as are the intricacies of a carburetor to a fledgling automobile driver.

In summary, if one wants to gain an understanding of Boolean algebra and its use in computer logic circuits, this is a good book to study. If one wants to gain a general understanding of 'thinking machines', this is not the right book. The subtitle of this book should be its title.

On the Rationalization of Sight. William M. Ivins, Jr. Da Capo, New York, 1973. 44 pp. + 2 annexes, illus. $18.00. Reviewed by F. H. C. Marriott:

For the late William M. Ivins, Jr., the discovery of the laws of perspective was the most important event of the Renaissance. With the development of engraving, it made possible the use of technical illustrations giving visual information in an unambiguous way. Who made the discovery is unknown, but it is clear that what was discovered was a set of rules for the guidance of artists, rather than mathematical theorems. In this sense, perspective antedated projective geometry.

The first known description of the 'costruzione legittima' was by Alberti in 1435-6. In 1505, Jean Pelerin ('Viator') published his illustrated guide to perspective drawing, De Artificiali Perspectiva, giving a slightly different, but equivalent, construction. Ivins discusses how these rules were discovered and gives a most convincing exposition of the way in which a simple model could be used to demonstrate each of the two constructions.

Albrecht Durer also wrote on perspective, but his description (1525) is wrong. Further, curious distortions appear in his work; in particular, his 'great showpiece of perspective rendering', the print of St. Jerome in his study (1514), is grossly out of perspective, if the room and furniture are supposed to have their ordinary shapes. Is it possible he had not studied perspective

**Dept. of Biomathematics, University of California, Los Angeles, CA 90024, U.S.A.

:Dept. of Biomathematics, University of Oxford, Pusey St., Oxford OX1 2JZ, England.

Angeles, CA 90024, U.S.A.

:Dept. of Biomathematics, University of Oxford, Pusey St., Oxford OX1 2JZ, England.

Angeles, CA 90024, U.S.A.

:Dept. of Biomathematics, University of Oxford, Pusey St., Oxford OX1 2JZ, England.

Angeles, CA 90024, U.S.A.

:Dept. of Biomathematics, University of Oxford, Pusey St., Oxford OX1 2JZ, England.

158 158 158 158 Books Books Books Books

This content downloaded from 195.34.79.20 on Sat, 14 Jun 2014 00:40:39 AMAll use subject to JSTOR Terms and Conditions