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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 and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...given straight line, similar to one given : 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 angles B and E equal, and AB : BC : : DE : EF, so that...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...a given straight line similar to one given ; and so on. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF, he similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...duplicate ratio of that which AB has to the homologous side FG. Wherefore, similar polygons, &c. Q. ED COR. 1. In like manner, it may be proved, that similar...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken AB has (10. def. 5,) to M the duplicate ratio of that which AB has to...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...proved that similar four-sided figures, or of any number of sides, are to one another as the squares of their homologous sides : and it has already been...universally, similar rectilineal figures are to one another as the squares of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, ,,,...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...the given figure, and similarly situated (vi.Def.i). PROP. XIX. THEOR. Similar triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous sides. Let A, D be equal angles, and AB, DE homologous sides of the similar triangles ABC, DEF ; and on AB,...
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Lectures Against Socialism: Delivered Under the Direction of the Committee ...

London City Mission - 1840
...testimony would suit the determination of such a case. If I want to determine whether similar triangles are to one another in the duplicate ratio of their homologous sides; the proper evidence will be to examine, by the powers of the mind, into the proofs which are alleged,...
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A new supplement to Euclid's Elements of geometry, by the author of 'A new ...

Joseph Denison - 1840 - 84 sider
...that proposition the nineteenth proposition of the sixth book of Euclid, viz. that similar triangles are to one another in the duplicate ratio of their homologous sides becomes turned into the following one, viz. that similar triangles are to one another as the squares...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles, each similar...
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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - 1841 - 184 sider
...other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their homologous...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...rectilineal figure of six, or any number of sides. 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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