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If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Elements of Geometry;: Containing the First Six Books of Euclid, with Two ... - Σελίδα 27
των John Playfair - 1795 - 400 σελίδες
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## Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 σελίδες
...SECTION IV. two angles of the one is equal to the sum of the remaining two angles of the other. 2. If two triangles have two angles of the one equal to two angles of the other, each to each, the third angle of the one is equal to the third angle of the other ; that is, the triangles are equiangular....

## Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 σελίδες
...and if the equal angles be subtracted from these equals, the remaining angles must be equal. M.—If two triangles have two angles of the one equal to two angles of the other, each to each, what may be said of the remaining third angles ? P.—They must be equal,—for the reason alleged...

## The Mechanical Euclid: Containing the Elements of Mechanics and Hydrostatics ...

William Whewell - 1837 - 182 σελίδες
...angle; therefore MLN is equal to LKH; and the angles at H and at N are right angles. Therefore the triangles have two angles of the one equal to two angles of the other ; and the side KL is equal to LM. Therefore the triangles are equal, and HL is equal to MN; that is,...

## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...be > Z EOF. PROPOSITION XXVI. (Argument ad absurdum). Theorem. If two triangles have two angles of one equal to two angles of the other, each to each, and one side equal to one side; viz., either the sides adjacent to the equal angles, or opposite to the equal...

## Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...by BD ; and because the right angle BED is equal to the right angle BFD, the two triangles EBD, FBD, have two angles of the one equal to two angles of the other ; and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 σελίδες
...is equal (const.) to FBD, and that the right angles BED, BFD are equal, the two triangles EBD, FBD have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore...

## Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ...

A. Bell - 1837 - 164 σελίδες
...Def. 7)i and therefore the angles AFG, AEG, are also equal. The triangles AGE, AGF, have therefore two angles of the one equal to two angles of the other, and they have also the side AG common ; wherefore they are equal, and the side AF is equal to the side...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...that the <UAx. right angle BED is equalt to the right angle BFD ; therefore the two triangles EBD, FBD have two angles of the one equal to two angles of , the other, each to each ; and the side BD, B Tf C •which is opposite to one of the equal angles in each, is common to both ; therefore...

## The Elements of Euclid

Euclid - 1838 - 416 σελίδες
...bisected by BD, and that the right angle BED is equal to the right angle BFD, the two triangles EBD, FBD have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each is common to both ; therefore...

## The Complete Mathematical and General Navigation Tables: Including Every ...

Thomas Kerigan - 1838
...the angle BCD, by the aforesaid proposition. And because the two triangles ADF and BCF have, thus, two angles of the one equal to two angles of the other, viz., the angle FAD to the angle FB C, and the angle AD F to the angle BCF; and the side AF of the...