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

Peter Nicholson - 1825 - 372 σελίδες
...takes place when in each triangle two sides respectively equal, form an equal angle ; and also when two angles of the one, equal to two angles of the other, are formed on an equal side. It is easy to demonstrate these propositions in the same manner as in...

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

Euclid, John Playfair - 1826 - 320 σελίδες
...the right angle BED, is equal to the right angle BFD, the two triangles EBD, FBD have two angli sof the one equal to two angles of the other ; and the side BD, whieh is opposite to one of the equal angles in eaeh, is eommon to both; therefore their other...

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

Robert Simson - 1827 - 513 σελίδες
...angle EBC: and the angle AEG is •15.1. equal* to the angle BEH: therefore the triangles AEG, BEH have two angles of the one equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another: • 26. 1....

The Complete Mathematical and General Navigation Tables: Including ..., Τόμος 1

Thomas Kerigan - 1828 - 664 σελίδες
...opposite angle CBF, — Euclid, Book I., Prop. 29. And, since the two triangles AFD and FBC have, thus, two angles of the one equal to two angles of the other, viz., the angle AFD to the angle FBC, and the angle FAD to the angle BFC, and the side AF of the one...

ELEMENTS OF GEOMETRY UPON THE INDUCTIVE METHOD.

JAMES HAYWARD - 1829
...mO' and M'N'O' are equal. The angle N'O'M' is common to the two triangles nmO' and N'M'O'; and having two angles of the one equal to two angles of the other, the other angles must be equal, that is, the angle O'M'N' is equal to the angle O' nm ; and this intersection...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
...angle DBF cannot but be equal to the angle DEG, that is, to ABC. And, because the triangles ABC, DEF have two angles of the one equal to two angles of the other, each to each, they are equiangular (1. 19. Cor. 1.), and therefore similar (31. Cor. 1.). Therefore,...

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 σελίδες
...be proved in all other triangles under the same conditions. Wherefore, universally, if two triangles have two angles of the one, equal to two angles of the other respectively ; &c. Which was to be demonstrated. PROPOSITION XXVII. THEOREM. — If a straight line...

The Moral Class Book, Or The Law of Morals: Derived from the Created ...

William Sullivan - 1833 - 352 σελίδες
...it. It is a truth, for example, but not a self-evident one, that if one draw two triangles, having two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either of the sides adjacent to the equal angles,...

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

Euclides - 1834
...and the right angle FHC equal to the right angle FKC, therefore in the triangles FHC, FKC there are two angles of the one, equal to two angles of the other, each to each ; and the side FC, which is opposite to one of the equal angles in each, is common to...

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

Euclid - 1835 - 513 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 Book IV. their...




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