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" 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 those angles equal which are opposite to the homologous sides. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Σελίδα 161
των John Keill - 1733 - 397 σελίδες
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 364 σελίδες
...fubtended the homologous Sides \ which was to be demonftrated. PROPOSITION VII, THEOREM. If there are two Triangles, having one Angle of the one equal to one Angle of the other , and toe Sides about other Angles proportional; and if the remaining third Angles are either both...

The Elements of Euclid: With Select Theorems Out of Archimedes

Euclid, André Tacquet - 1727 - 239 σελίδες
...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...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 σελίδες
...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...

Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid, Edmund Stone - 1765 - 464 σελίδες
...rectangle under c E and cc, fo is the parallelogram AC, to the parallelogram cr . WWD If fhe're be two triangles having one angle of the one equal to one angle of the other : thofe triangles will be to one an•other in the ratios compounded of the ratio of the fides containing...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 σελίδες
...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...

The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - 1775 - 159 σελίδες
...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...

The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 264 σελίδες
...; therefore DEF is 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...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 σελίδες
...Wherefore, if two triingles, &c. Q^ED La PROP. Book Vt. V-'V"0 PROP. VII. THEO R. IF tw6 triangles have one angle of the one equal to one angle of the other, and the fides about two other angles proportionals, then, if each of the remaining angles be either...

Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - 1782 - 399 σελίδες
...and the Sides that are about the equal Angles reciprocal) - are equal, which was to be demonftrated. PROPOSITION XV. THEOREM. Equal Triangles, having one Angle of the one equal to one Angle of the clber, leave, tbrir Sides about the equal Angles reciprocal ; and tbofe Triangles that have one Angle...

Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - 272 σελίδες
...with the triangle AGH (I. 7.) or ABC, as was to be fhewn. PROP. VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF...




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