Books Books If two triangles have two sides of the one equal to two sides of the... Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 9
by Euclides - 1842 ## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...conditions. Wherefore, universally, if two triangles have two sides &c. Which was to be demonstrated. THEOREM. — If two triangles have two sides of the one, equal to two sides of the other respectively, but the third side of the one is greater than the third side of the other ; the... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...greater than EF. Therefore, " if two triangles," &c. QED PROP. XXV. THEOR. If two triangles have tiro sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides... ## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...another in each of the points С, Е. Join AC, AE, В С, BE. Then because the triangles AD С, ADE have two sides of the one equal to two sides of the other, and have also the included angles ADC, ADE equal to one another, the base А С (I. 4.) is equal... ## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...has just been found that BO + OC< BD + DC ; therefore, still more is BO + OC<BA+AC. PROPOSITION IX. THEOREM. If two triangles have two sides of the one...equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...shall be less than the other two sides of the triangle, but shall contain a greater angle. XXIV. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of the one greater than the angle contained by the two sides... ## The Schoolmaster: Essays on Practical Education, Selected from the ..., Volume 1

Education - 1836 - 502 pages
...as possible, and also of many superfluous phrases. For instance, " if there be two triangles which have two sides of the one equal to two sides of the other, each to each, &c." The phrase in italics is not an English idiom, but the literal translation of the Greek twrepa.... ## The schoolmaster: essays on practical education, selected from the works of ...

Schoolmaster - 1836 - 926 pages
...as possible, and also of many superfluous phrases. For instance, " if there be two triangles which have two sides of the one equal to two sides of the other, each to each, &c." The phrase in italics is not an English idiom, but the literal translation of the Greek '.y.xrepa.... ## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...which the vertex of one triangle is upon a side of the other, needs no demonstration. PROPOSITION VIII. THEOREM. If two triangles have two sides of the one...sides of the other, each to each, and have likewise their bases equal, the angle which is contained by the two sides of the one shall be equal to the angle... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...line equal to A 15. the line € might be produced, till it and the part added would be equal to AB. PROP. IV. THEOREM. IF two triangles have two sides...one equal to two sides of the other, each to each ;t and have also the angles contained by those sides equal to one another : (!..) they have likewise... 