Books Books Any two sides of a triangle are together greater than the third side. The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 16
by Euclides - 1814 ## Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Geometry - 1828 - 180 pages
...neither equal nor less than AB, it must be greater than it; as was to be demonstrated. § 19. THEOREM. Two sides of a triangle are together greater than the third side. APPLIC. Let ABC, (fig. 26.) be a triangle, the two sides AC, and CB, taken together, are greater than... ## The Geometrical Companion, in which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 190 pages
...the side which the sparrow has to fly in proportion to that which it has to fly itself. ART. 43. " Any two sides of a triangle are together greater than the third sidr." As I have observed before, we often, without knowing an angle from a triangle, give an involuntary... ## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...AB; therefore AC is greater than AB. Wherefore, the greater angle &c. QED PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than...third side. Let ABC be a triangle; any two sides of it are together greater than the third side, namely, the sides BA, AC are greater than the side BC ; and... ## Self-examinations in Euclid

John Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...right angles; .-. angles A, ABC are together < than two right angles. PROP. XX. 56. To prove that ' any two sides of a triangle are together greater than the third side,' what is the general construction ? From the point where they meet, produce either of the two sides... ## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 1 0. (Eue. i. 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...equal to AB; therefore AC is greater than AB. Wherefore the greater angle, &c. QE D PROP. XX. THEOR. I Any two sides of a triangle are together greater than...side, viz. the sides BA, AC greater than the side BC j and AB, BC greater than AC; andBC, CA greater than AB. Produce BA to the point D, and make (3. 1.)... ## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...BE, EC. But AE, EC are equal to AC; therefore BA, AC are together greater than BE, EC. Again, because two sides of a triangle are together greater than the third side, EC and ED are together greater than CD. To each of these add DB; therefore EC, ED, DB are together... ## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...is not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 10. (Eue. L 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...angle of every triangle is subtended by the greater side, or has the greater side opposite to it. XX. Any two sides of a triangle are together greater than the third side. XXI. If from the ends of one side of a triangle, there be drawn two straight lines to a point within... 