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 Książki Książki SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. The Elements of Euclid; viz. the first six books, together with the eleventh ... - Strona 165
autor: Euclides - 1814
Pełny widok - Informacje o książce ## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...rectilineal figure may be described upon a given straight line, similar to one of six or more sides. Similar triangles are to one another in the duplicate ratio of their homologous sides. Given that ABC and DEF are similar triangles, having the angle B equal to the angle E, and AB to BC...
Pełny widok - Informacje o książce ## REPORT OF THE DIRECTOR OF PUBLIC INSTRUCTION, BOMBAY, FOR THE YEAR 1858-59.

...has to the fourth ? 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...
Pełny widok - Informacje o książce ## The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...homologous sides are parallel. PROPOSITION XIX. THEOREM. — If triangles (ABC, DEF) are similar, they are to one another in the duplicate ratio of their homologous sides (BC, EF). CONSMHTCTION. Take BG a third proportional to BC, EF (a), so that BC is to EF, as EF f* to...
Pełny widok - Informacje o książce ## Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...— to Plans, 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...
Pełny widok - Informacje o książce ## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - Liczba stron: 12
...less than a 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...
Pełny widok - Informacje o książce ## Wisconsin Journal of Education, Tom 7

1863
...^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...
Pełny widok - Informacje o książce ## Papers Read at the Royal Institute of British Architects

1863
...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...
Pełny widok - Informacje o książce ## The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...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...
Pełny widok - Informacje o książce ## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...angles proportionals, they are similar to one another. In the same manner a rectilineal figure of six sides may be 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...
Pełny widok - Informacje o książce ## The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...proportionals ; wherefore AB3&HG la similar to CDKEF. In the same manner a rectilineal figure of six sides [may 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...
Pełny widok - Informacje o książce