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" Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 180
av Robert Simson - 1806 - 518 sider
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 sider
...homologous sides : and it has already been proved in triangles : therefore, universally, similar rectilinear figures are to one another in the duplicate ratio of their homologous sides. (629) COR. 2. — And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...CoB. 1. In like manner it may be proved that similar figures of four sides, or of any number of sides, are to one another in the duplicate ratio of their homologous sides; and it has been proved in triangles. Therefore, universally, similar rectilineal figures are to one...
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University of Cambridge - 1830
...intensity. SATURDAY MORNING .... 9 to 11. First, Second, Third and Fourth Classes. 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 2. If two straight lines meeting one another, be parallel to two straight lines which meet one another,...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...homologous sides of the figures, are to one another, each to eich, in the same ratio. But similar triangles are to one another in the duplicate ratio of their homologous sides. Therefore the triangles into which the figure А В С DEF is divided, are to the similar triangles...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...to another in the duplicate ratio of their homologous sides; and the same has already been proved of triangles: therefore, universally similar rectilineal...in the duplicate ratio of their homologous sides. COH. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 sider
...same has already been proved of triangles : therefore, universally similar rectilineal figures are,to one another in the duplicate ratio of their homologous...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def. 11. 5.) to 1VI the duplicate ratio of that which AB has...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...similar triangles are to one another as the squares of their homologous sides. PROP. 43. (Eue. vi. 20.) Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides ; and their perimeters are as those sides. For it has been seen (32. Cor. 2.) that any two similar...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...another, in the duplicate ratio of their homologous sides ; and the same has already been proved of triangles : therefore, universally similar rectilineal...in the duplicate ratio of their homologous sides. 2. And universally, it is manifest, that if three straight lines be proportionals, as the first is...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles having the angle B equal to the angle E, and let AB be to BC, as...
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