A History of Elementary Mathematics With Hints On Methods of Teaching
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It was in eight books ; the first and parts of the second are now missing. The object of this treatise appears to have been to supply geometers with a succinct analysis of the most difficult mathematical works and to facilitate the study of these by explanatory lemmas. It is invaluable to us on account of the rich information it gives on various treatises by the foremost Greek mathematicians, which are now lost. Scholars of the last century considered it possible to restore lost works from the ...rhiime given by Pappus alone. Some of the theorems are doubtless original with Pappus, but here it is difficult to speak with certainty, for in three instances Pappus copied theorems without crediting them to the authors, and he may have done the same in other cases where we have no means of ascertaining the real discoverer.
Of elementary propositions of special interest and probably GREECE 87 his own, we mention the following : (1) The centre of inertia (gravity) of a triangle is that of another triangle whose vertices lie upon the sides of the first and divide its three sides in the same ratio ; (2) solution of the problem to draw through three points lying in the same straight line, three straight lines which shall form a triangle inscribed in a given circle ; ^ (3) he propounded the theory of involution of points ; (4) the line connecting the opposite extremities of parallel diameters of two externally tangent circles passes through the point of contact (a theorem suggesting the consideration of centres of similitude of two circles) ; (5) solution of the problem, to find a parallelogram whose sides are in a fixed ratio to those of a given parallelogram, while the areas of the two are in another fixed ratio.
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To quickly assess the difficulty of the text, read a short excerpt:
It was in eight books ; the first and parts of the second are now missing. The object of this treatise appears to have been to supply geometers with a succinct analysis of the most difficult mathematical works and to facilitate the study of these by explanatory lemmas. It is invaluable to us on account of the rich information it gives on various treatises by the foremost Greek mathematicians, which are now lost. Scholars of the last century considered it possible to restore lost works from the ...rhiime given by Pappus alone. Some of the theorems are doubtless original with Pappus, but here it is difficult to speak with certainty, for in three instances Pappus copied theorems without crediting them to the authors, and he may have done the same in other cases where we have no means of ascertaining the real discoverer.
Of elementary propositions of special interest and probably GREECE 87 his own, we mention the following : (1) The centre of inertia (gravity) of a triangle is that of another triangle whose vertices lie upon the sides of the first and divide its three sides in the same ratio ; (2) solution of the problem to draw through three points lying in the same straight line, three straight lines which shall form a triangle inscribed in a given circle ; ^ (3) he propounded the theory of involution of points ; (4) the line connecting the opposite extremities of parallel diameters of two externally tangent circles passes through the point of contact (a theorem suggesting the consideration of centres of similitude of two circles) ; (5) solution of the problem, to find a parallelogram whose sides are in a fixed ratio to those of a given parallelogram, while the areas of the two are in another fixed ratio.
What to read after A History of Elementary Mathematics With Hints On Methods of Teaching?
You can find similar books in the "Read Also" column, or choose other free books by Florian Cajori to read onlineMoreLess
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