Books Books If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 143
by Euclid, James Thomson - 1837 - 390 pages ## The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844
...this line makes with the touching line, shall be equal to the angles in the alternate segments. 12. If two triangles have one angle of the one equal to...the sides about the equal angles proportionals, the triangles shall be equiangular. MECHANICS AND HYDROSTATICS. MONDAY, JANUARY 15. 9.. .12. MR. HATHIBON,... ## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... ## A system of practical mathematics; being no.xvi. of a new series of school-books

...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of... ## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and conversely, parallelograms... ## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3.... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional ; And triangles which have one angle... ## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...parallelogram BC. Wherefore, Equal parallelograms *rc. QED PROP. XV. THEOR. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and triangles, which have one angle... ## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...of two triangles, &c. QED Kecite (a) p. 23, 1; Wp.9,5; (4) 32, 1 ; (Op.8,1: p. 4, 6; ax. 1,1. 6 Th. If two triangles have one angle of the one equal to one of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,... ## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...(c)p. 8, 1; (c)p. 4, 6; (/)ax. 1, 1. 6 Th. If two triangles have one angle of the one equal to one of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite homologous sides.... 