Books Books 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 ## Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 68 pages
...hand, equal triangles Prop. xii. upon the same base (or upon equal bases in the same straight line) and upon the same side of it, are between the same parallels. For if the straight line which joins the vertices of the two triangles be not parallel to the base,... ## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...in the circumference which bisectsthe angle between them.] (c) The vertices of all equal spherical triangles upon the same base and upon the same side of it, lie in the circumference of a small circle, such that one equal and parallel to it may be drawn through... ## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XL. See Note. THEOREM. — Equal triangles, upon equal bases in ihe same straight line, and on the same side of it, are between the same parallels. Let the triangles ABC, EFD, which are upon equal bases BC and EF in the same straight line BF, and on the same... ## The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...is equal to the • 7 Ax. triangle DEF. Wherefore, triangles, &c. QED PROPOSITION XXXIX. THEOn. — Equal triangles upon the same base, and upon the same...Join AD : AD shall be parallel to BC. For if it is not, through the point A, draw * AE parallel to BC, and join EC. s 31. i. The triangle ABC is equal... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...the triangle ABC is equal to the triangle DEF. Wherefore, " triangles" &c. QED PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same...the same base BC, and upon the same side of it; they are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the * point... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...(7. Ax.) ; therefore the triangle ABC is equal to the triangle DEF. PROP. XXXIII. THEOR. Equivalent triangles upon the same base, and upon the same side...same base BC, and upon the same side of it ; they are between the same parallels. Join AD : AD is parallel to BC ; for, if it is not, through the point... ## Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...in the circumference which bisects the angle between them.] (c) The vertices of all equal spherical triangles upon the same base and upon the same side of it, lie in the circumference of a small circle, such that one equal and parallel to it may be drawn through... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...XXXVIII. Triangles upon equal bases, and between the same parallels, are equal to one another. XXXIX. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. XL. Equal triangles on the same side of bases, which are equal and in the same straight line, are between... ## A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 128 pages
...equal, 24. ART. 26. Triangles upon equal bases and between the same parallels are equal, ibid. ART. 27. Equal triangles upon the same base, and upon the same side of it, are between the same parallels, '25. ART. 28. Parallelograms which have equal bases and equal altitudes ire equal, 26. ART. 29. Triangles... 