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" EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 40
by Euclides - 1841 - 351 pages
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 318 pages
...things are equal (7. Ax.) ; therefore the triangle ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same...equal triangles ABC, DBC be upon the same base BC, and uoon the same side of it ; they are between the same parallels. "Join AD ; AD is parallel to BC ; for,...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...the point G will coincide with F, and the line EG with EF; wherefore EG or BC is equal to E F. XLII. Equal triangles upon the same base, and upon the same...between the same parallels. Let the equal triangles ABC, DBG (Fig. 33) be upon the same base BC, and upon the same side of it ; they are between the same parallels....
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...CHEB. the triangle AB ( ' has been bisected from the point H by the line HE. QKF PROP. 39.— TIIEOR. Equal triangles upon the same base and upon the same side of it are between the same parallels. CONSTRUCTION. — Pst. 1. A line may be drawn between two points. 1*. ,-il. Through a given point to...
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Parliamentary Papers, Volume 7

Great Britain. Parliament. House of Commons - Bills, Legislative - 1859
...ad absurdum, and illustrate it by Euclid, Book I., Prop. 39, "Equal triangles, upon the same4Sase, and upon the same side of it, are between the same parallels." Is the reducuo adabstirdnmofless force than the direct forms of inference ? 3. Construct an isosceles...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base and upon the same...upon the same base BC and upon the same side of it. Then the triangles ABC, DBC shall be between the same parallels. AD Join AD ; then AD shall be parallel...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...equal (Ax. 7) ; therefore the triangle ABC is equal to the triangle DEF. PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Given the equal triangles ABC and DBC, upon the same base BC, and upon the same side of it; to prove...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...to one another; and those to which the same M has the some R are eq. to one another. 39, 1. Eq. Дs upon the same base and upon the same side of it are between the same parallels. E. l C. Hyp. 1. Cone. C. CASE I. Let DE be [| BC, one of the sides of Д ABC; and let DE cut the other...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...Parallelograms which have two sides and the included angle equal in each, are themselves equal. 22. Equivalent triangles upon the same base, and upon the same side of it, are between the same parallels. 23. If the middle points of the sides of a trapczoid, which are not parallel, be joined by a straight...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...Parallelograms which have two sides and the included angle equal in each, are themselves equal. 22. Equivalent triangles upon the same base, and upon the same side of it, are between the same parallels. 23. If the middle points of the sides of a trapezoid, which are not parallel, be joined by a straight...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863
...obtained ; the product of the base and altitude gives the area of a parallelogram : PROP. 39. — TIIEOK. Equal triangles upon the same base and upon the same side of it are between the same parallels. CON.— Pst.'l, P. 31.— DEM.— P. 37, Ax. 1. Letthe AS ABC, qual, ittne ASAUU, -Lii3u,De equal,...
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