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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: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 163
by Robert Simson - 1762 - 466 pages

## Report on Education in the Parochial Schools of the Counties of Aberdeen ...

...angles." ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar...

## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 350 pages
...5.) : wherefore 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 ih* other have their sides about the equal angles reciprocally proportional ; And triangles which have...

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and triangles which 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 ABC,...

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and triangles which 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 ABC,...

## The Edinburgh university calendar

Edinburgh univ - 1868 - 336 pages
...rectangle contained by the segments of the other. 4. To inscribe a circle in a given triangle. 5- 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. 6. Find the continued product of (x + y + z),...

## The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volume 4

Mathematics - 1868 - 272 pages
...Let the lines joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the triangles...

## Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 172 pages
...equiangular to A' B'C' ; Therefore ABC is equiangular to A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC'...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. 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...