 | Sir James Kay-Shuttleworth - 1853 - 554 σελίδες
...the base, the triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms have to one... | |
 | Euclides - 1853 - 176 σελίδες
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. LET ab,... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...equiangular to the triangle DEF. Wherefore, if the sides, etc. QED PROPOSITION VI. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | Euclides - 1853 - 334 σελίδες
...has been found a mean proportional HE. Which was to be done. PEOP. XIV. THEOE. If two parallelograms, which have one angle of the one equal to one angle of tie other, be equal : then they shall have their sides about this pair of equal angles reciprocally... | |
 | Euclides - 1855 - 270 σελίδες
...parallels passes through the extremities of all the parallels. PROP VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about another angle in each, proportionals ; and if the remaining angle in each be of... | |
 | 1855 - 264 σελίδες
...the hase shall have the same ratio which the other sides of thi; triangle have. 2. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles bhall be equiangular, and shall have... | |
 | British and foreign school society - 1857 - 548 σελίδες
...are due to the eighteenth century? HIGHER MATHEMATICS AND MATHEMATICAL PHfSÏCg. 1. If two triangles have one angle of the one equal to one angle of the other atid the sides "aboiift two other angles proportional ; then if each of the remaining angles be less... | |
 | 1871 - 420 σελίδες
...the proposition and reduces it to a case of ambiguous equality. Let the triangles ABC, DEF (fig. 9) have one angle of the one equal to one angle of the other; namely, L ВАС =¿ DEF, and the sides about two other angles ABC, EDF proportionals, so that AB :... | |
 | 1857 - 486 σελίδες
...and the angle in a segment less than a semicircle is greater than a right angle. 9. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | War office - 1858 - 578 σελίδες
...of the angles at the base double of the third angle. 8 DIRECT COMMISSIONS. 2. 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. Show also how this follows from the arithmetical... | |
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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. 
