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" FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 136
των Euclid, John Playfair - 1826 - 320 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 σελίδες
...FGHKL, the angle BAE is equal to the angle GFL *, and BA is to AE, as GF to FL ". wherefore becaufe the triangles ABE, FGL have an angle in one equal to an angle in the other, i find their fides about thefe equal angles proportionals, the triangle ABE is equiangular b, and therefore...

Elements of Geometry

abbé Rossignol (Jean-Joseph) - 1787 - 162 σελίδες
...would be 5 identical ; 'which is abfurd, fmce their angles are unequal. PROP. LXIIH * Triangles which have an angle in one equal to an angle in the other, and the fides about thefe angles proportional, are equiangular. If, in the two triangles BAC, NMP, the...

Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 σελίδες
...BAE is equal i ». def. 6. to the angle GFL a, and BA is to AE, as GF to FL " : wherefore, becaufe the triangles ABE, FGL have an angle in one equal to an angle in the other, and their fides about theft thefe equal angles proportionals, the triangle ABE is equi- BookV^ angular b, and...

The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 σελίδες
...FGHKL, the angle BAE is equal to GFL », anda i.Def.6. BA is to AE, as GF to FL a : Wherefore, becaufe the triangles ABE, FGL have an angle in one equal to an angle in the other, and their fides about thefe angles proportionals, the triangle ABE is equiangular b, and therefore fimilar to...

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

Robert Simson - 1806 - 518 σελίδες
...» : wherefore, be- *— v— ^ cause the triangles ABE, FGL have an angle in one equal toa1.def.6. an angle in the other, and their sides about these...angles proportionals, the triangle ABE is equiangular b, and therefore b 6. 6. similar to the triangle FGLc; wherefore the angle ABE isc4. 6. equal to the...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...Boon Vf. BAE is equal to the angle GFL a , and BA is to AE, as *~~*~** GFtoFL3: Wherefore, because the triangles ABE, FGL "' "' " have an angle in one equal to an angle in the other, and theirsidesaboutthese equal angles proportionals, the triangle ABE is equiangular b , and therefore...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...BAE is equal to the angle GFLa, mid BA is to AE, as ^TT* GFtoFL": Wherefore, because the trianglc.s ABE, FGL " ""' "' have an angle in one equal to an angle in the other, and their sidesabout these equal angles proportionals, the triangle ABE is equiangular11, and therefore similar,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 σελίδες
...angle BAE is equal to the angle GFL(1. def. 6.),andBA is to AE,asGF to FL(1. def 6.); wherefore because the triangles ABE, FGL have an angle in one equal...angles proportionals; the triangle ABE is equiangular (6.6.J, and therefore similar to the triangle FGL (4. 6.;; wherefore the angle ABE is equal to the...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...equal to the angle GFL, (1, def. 6.) and BA is to AE, as GF to FL: (1. def. 6.) Wherefore, because the triangles ABE, FGL, have an angle in one equal...proportionals, the triangle ABE is equiangular, (6. в.) and therefore similar to the triangle FGL : (t. 6.) Wherefore the angle ABE < equal to the angle...

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

Robert Simson - 1827 - 513 σελίδες
...angle GFL, and BA is to AE*, » 1 D(* 6. as GF to FL : therefore, because the triangles ABE, 1 Def. 6. FGL have an angle in one equal to an angle in the other, and their sides about these equal angles, propor* 6. 6. tionals, the triangle ABE is equiangular* to the triangle * 4. 6. FGL ; and therefore*...




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