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" ... rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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A Treatise on Practical Mensuration

Anthony Nesbit - 1859 - 494 páginas
...triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate , ratio of their homologous sides. (Euc. B VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle the double of the square of...
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Elements of Geometry and Mensuration: With Easy Exercises, Designed for ...

Thomas Lund - 1859 - 362 páginas
...tt/ DX * Sometimes called 'homologous sides'. 'f- Euclid's enunciation of this is: 'Similar triangles are to one another in the duplicate ratio of their homologous sides'. X zB=z&, zC=zc; then AB, ab being any two corresponding, or homologous, sides, the triangle ABC shall...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 páginas
...AB has to the homologous side FG. COR. 1. — In like manner it may be proved that similar foursided figures, or of any number of sides, are one to another...duplicate ratio of their homologous sides. COR. 2. — If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V. Def. 18)...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 páginas
...another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal...in the duplicate ratio of their homologous sides. COROLLARY 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 páginas
...duplicate ratio of their homologous sides : and it has already been proved in triangles : (vI. 19.) therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. CoB. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vI. 11.) AB...
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REPORT OF THE DIRECTOR OF PUBLIC INSTRUCTION, BOMBAY, FOR THE YEAR 1858-59.

EDUCATION SOCIETY'S PRESS, CULLA - 1860
...The sides about the equal angles of equiangular triangles are proportionals. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. LOGIC. I.—LOWER STANDARD. What ii the use of words ? Explain First and Second Intention. 2. Give...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 páginas
...semicircle is greater than a right angle. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a rectilineal figure which shall be similar to one given rectilineal figure and equal to...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...Maps, and Geometrical Drawings of every kind. PROP. 19. — THEOR. (Very important.) Similar triangles are to one another in the duplicate ratio of their homologous sides ; ie, as the squares of their like sides. CON. 11, VI. DEM. Def. 12, V.— 16, V. If four Ms of of...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...rectilineal figure of six sides; and so on. QEF PEop. XIX. (THEOHEM.)—Similar triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous sides. Let the angle ABC be equal to the angle DEF, and let AB be to BC as DE to EF, so that the side BC is...
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Wisconsin Journal of Education, Volumen7

1863
...the triangle ABC. I should mention 2 to draw ox parallel to BG. Now we know that similar triangles are to one another in the duplicate ratio of their homologous sides . • . BGC : oxC::BGa : ox', or 47.04 : 42::11.2" : 112 the square root of which is 10.583+=ox, or...
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