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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. "
The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ... - Page 163
by Robert Simson - 1804
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Euclid's Elements of geometry: from the Latin translation of Commandine. To ...

John Keill - Logarithms - 1723 - 364 pages
...reci frotalt are equal between themfelves. if - • • . * • T ET the equal Triangles ABC, ADE, have one •*-' Angle of the one equal to one Angle of the other, viz the Angle BAC equal to the Angle DAE. I lay the Sides about the equal Angles are reciprocal, th.it...
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The Elements of Euclid; with select theorems out of Archimedes

Euclides - Mathematics - 1727
...the firft Part. i PROP. XXVI. Theorem. IF two Triangles (XandZ) have two Angles equal&g. 2;. to two, one Angle of the one equal to one Angle of the other ( B to F and C to /), and one Side of one Equal to one of the other, whether it be that •which is...
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Euclid's Elements of geometry: from the Latin translation of Commandine. To ...

John Keill - Trigonometry - 1733 - 397 pages
...is equal to the Angle GFL ; and BA is to AE, as GF is to F L. Therefore the two Triangles BAE, GFL, have one Angle of the one equal to one Angle of the other, viz. the Angle BAE equal to the Angle GFL, and the Sides about the equal Angles proportional. Wherefore...
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...equiangular to the triangle DEF. Wherefore if the fides, &c. Q^ED PROP. PROP. VI." THEOR. TF two triangles have one angle of the one equal to one angle of the other, and the fides about the equal angles proportionals, the triangles fhall be equiangular, and fhall have...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclides, David Gregory - Mathematics, Greek - 1765 - 464 pages
...and accordingly the triangles ABC, DBF are equiangular. . .v : ... .- ..: If therefore two triangles have one angle of the one equal ,to one angle of the othsr, and the fides about two other angles proportional, and have alfo each of the remaining angles...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - Geometry - 1772 - 399 pages
...are equal; which was to be demonftrated. tl PROPOSITION XV. . ry, 1 HEORE M. Equal Triangles, having one Angle of the one equal to one Angle of the other, have tbeir ' Sides about tbe equal Angles reciprccal ; and thofe -Triangles that have one Angle of the one...
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The Elements of Euclid, viz: The errors, by which Theon, or others, have ...

Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...the triangle DEF. Wherefore, if the fides, &c. QED PKOP. Book VI. PRO P. VI. THEO R. TF two triangles have one angle of the one equal to one angle of the other, and the ftdes about the equal angles proportionals, the triangles Shall be equiangular, and fhall have...
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The geometrician: containing essays on plane geometry, and trigonometry ...

Benjamin Donne - Mathematics - 1775 - 159 pages
...Angle in one is equal to the remaining Angle in the other Triangle. 8 1. Co ROLL. 3. If two Triangles have one Angle of the one equal to one Angle of the other, then the Sum of the two remaining Angles of one Triangle is equal to the Sum of the two remaining Angles...
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The Elements of Euclid: in which the propositions are demonstrated in a new ...

Euclid - Geometry - 1776 - 264 pages
...fides about the equal angles reciprocally proportional-, and theje parallelograms and triangles that have one angle of the one equal to one angle of the other , and the fides about the equal angles reciprocally proportional 9 are equal, viz. the parallelogram...
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The Elements of Euclid: in which the propositions are demonstrated ..., Book 11

Euclid - Geometry - 1776 - 264 pages
...likewife equiangular to ABC. Wherefore, &c, PRO P. VII. THEO R. TF there are two triangles, having one angle of the one equal •*• to one angle of the other, and the fides about afecond angle of the one proportional to the fides about the correfpondent angle...
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