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" If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let... "
The Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 232
των Euclides - 1874
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Calendar of Dalhousie College and University

Dalhousie University - 1884 - 184 σελίδες
...of which the well-known 47th Proposition of Book I. is a special case. 2. If two triangles that have two sides of the one proportional to two sides of the other, are capable of being joined at one angle so that the homologous sides are parallel, the remaining sides...

The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 σελίδες
...Prove As ABE, ADE similar, and that EC bisects L BED. PROPOSITION 7. THEOREM. If two triangles have two sides of the one proportional to two sides of the other, and the angles opposite to one pair of homologous sides equal, the angles opposite to the other pair...

The Elements of Geometry

George Bruce Halsted - 1885 - 389 σελίδες
...491, BD = BC, .-. £ C = 4 BDC. But 4 BDC + £ BDA = st. £, 513. COROLLARY. If two triangles have two sides of the one proportional to two sides of the other, and an angle in each opposite one corresponding pair of these sides equal, then if one of the angles...

The Elements of Geometry

George Bruce Halsted - 1886 - 394 σελίδες
...491, BD = BC, .-. 4 C = 4 BDC. But £ BDC + 4 BDA — st. £, 513. COROLLARY. If two triangles have two sides of the one proportional to two sides of the other, and an angle in each opposite one corresponding pair of these sides equal, then if one of the angles...

Elements of Quaternions

Arthur Sherburne Hardy - 1887 - 264 σελίδες
...PD, BP = PA. 3. If two triangles, having an angle in each equal and the including sides proportional, be joined at one angle so as to have their homologous sides parallel, the remaining sides will be in a straight line. Let (Fig. 9) AB = a, AE = /3. Then, Flg• 9by condition,...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...740 quadl. ANBO= AABL ; ?«a<#. AOBL. = ABDL. PROPOSITION 32. THEOREM. If two triangles which have two sides of the one proportional to two sides of...the remaining sides shall be in a straight line. Let FGA, ABC be two AS such that FG : GA :: AB : BC, and let FG, GA be || to AB, BC respectively; then...

Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 442 σελίδες
...on AB : sq. on AC, = Z: Y. . . X + Y = Z. EUCLID Proposition 32. THEOREM — If two triangles have two sides of the one proportional to two sides of the other, and are so placed at an angle that tJie homologous sides are parallel, the remaining sides of the triangles...

Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - 1904 - 324 σελίδες
...from a given tangent a sect any multiple of the segment between 0 and tangent. Ex. 280. If 2 As have two sides of the one proportional to two sides of the other, and ^. s, one in each, opposite one corresponding pair of these sides = , the ^ s opposite the other...

Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - 1904 - 322 σελίδες
...from a given tangent a sect any multiple of the segment between O and tangent. Ex. 280. If 2 AS have two sides of the one proportional to two sides of the other, and ^ s, one in each, opposite one corresponding pair of these sides = , the ^ s opposite the other...

The Dublin University Calendar, Τόμος 1

Trinity College (Dublin, Ireland) - 1907 - 536 σελίδες
...a circle are equal to the angles in the alternate segments of the circle. 8. If two triangles have two sides of the one proportional to two sides of the other, and the angles opposite one pair of corresponding sides equal, prove that the angles opposite the other...




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