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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 117
by Thomas Gaskin - 1847 - 263 pages
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Papers Read at the Royal Institute of British Architects

Architecture - 1863 - 300 pages
...scale of equal parts how a rule of three sum may be solved geometrically. 9. Proposition 19. Theorem. Similar triangles are to one another in the duplicate ratio of their homologous sides. J 0. If the superficial content of a triangle which has a base of 40 feet is 800 feet, what is the...
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Wisconsin Journal of Education, Volume 7

Education - 1863 - 406 pages
...^5-^— 9=42 or 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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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...and this has been proved of triangles (VI. 19); therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2.-—If to AB and FG, two of the homologous sides of the polygon, a third proportional M bo taken...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...described upon a given straight line similar to one given, and so on. QE r. PROPOSITION XIX. THEOREM. 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. 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 bo to BC, as...
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A Rudimentary Treatise on Land and Engineering Surveying, with all the ...

Thomas Baker (Civil engineer) - 1865 - 278 pages
...then, the triangle ABC is to the triangle AED as the square of AB is to I lie. square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...be described upon a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. Similar triangles are to one another in the duplicate ratio of their homologous sides. (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles, having...
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Calendar of the McGill University, Montreal

McGill University - 1865 - 332 pages
...proportion, and show that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours each will...
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Rudimentary treatise on mensuration and measuring

Thomas Baker (C.E.) - 1865 - 174 pages
...greatest angle : theorem, 17 ; any two angles being Rven, the, becomes known : theorem, ' ; similar, are to one another in the duplicate ratio of their homologous sides: theorem, 17. Triangular prism, definition of, 52. Triangular fields, method of surveying with chain...
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 428 pages
...together with the segmenta of the former will be equal to the square of the radius of the circle. i 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. If two straight lines be at right angles to the same plane, they shall be parallel to one another....
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