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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. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Σελίδα 66
των John Keill - 1733 - 397 σελίδες
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 σελίδες
...equal to KCF, and the right angle FHC equal to the right angle FKC; in the triangles FHC, FKC there are two angles of the one equal to two angles of the other, and the side FC, which is opposite to one of the equal angles in each, is common to both : therefore the other sides...

Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...to А В С, and let the line EG meet DF, or DF produced in G. Then, because the triangles ABC, DEG have two angles of the one equal to two angles of the other, each to each, they are equiangular : therefore (31.) DE : EG ••AB: В С, but AB:BC::DE:EF: therefore...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...therefore all the exterior angles are equal to four right angles. PROP. VI. THEOR. 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, the triangles shall be equivalent. Let ABC, DEF be two...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...greater base, shall be greater than the angle contained by the sides of the other. XXVI. 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 angles,...

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

William Whewell - 1837 - 182 σελίδες
...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, to RS. In the...

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

John Playfair - 1837 - 318 σελίδες
...GNK, and the angles GMK, GMN are both right angles by construction ; wherefore, the triangles GMK. GMN have two angles of the one equal to two angles of the other, and they have also the side GM common, therefore they are equal(26. l.),andthe side KM is equal to the...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...therefore the angle BAC is greater than the angle EDF. PROPOSITION XXVI. THEOREM. 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 ; namely, either the sides adjacent to the equal angles,...

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...

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

Charles Reiner - 1837 - 215 σελίδες
...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...

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

Euclid, James Thomson - 1837 - 390 σελίδες
...all equal. Hence (I. 6.) CH is equal to HD, DK to KE, &c. Also, in the triangles CHD, DKE, there are two angles of the one equal to two angles of the other, and (hyp.) the sides CD, DE, are equal : therefore (I. 26.) the sides CH, HD are equal to DK, KE, each...




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