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As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.

As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.

As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.

As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.

As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.

As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.