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 ## The Elements of Plane and Spherical Trigonometry

John Hind - Trigonometry - 1855 - 546 pages
...excluded. The circumstances here pointed out, are nothing more than what have all along been assumed, that any two sides of a triangle are together greater than the third : but it thus appears that the Algebraical Formulae are sufficient of themselves to determine the consistency... ## The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...opposite the greater of the two AB, AC, or, in other words, AC is greater than A B. XXI.— EUCLID I. 20. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle (Fig. 14), take any side BA and produce it at one extremity to D,- making AD equal to AC the adjacent... ## The British and Foreign Evangelical Review and Quarterly Record of Christian ...

Theology - 1856 - 984 pages
...of its conclusions. They who can deny them, * Jxdtptndent for June 28, 1855. may as well deny that any two sides of a triangle are together greater than the third side, or the truth of any other demonstrable proposition.* What was the peculiar characteristic nature of... ## Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...angles at the base, prove that the locus of the vertex is a hyperbola, and find its asymptotes. 1. ANY two sides of a triangle are together greater than the third side. If a polygon with only salient angles be situated inside another polygon, the perimeter of the former... ## The Popular Educator, Volume 1

1856 - 422 pages
...restriction is plain, when we consider that he had previously proved in his Prop. XX., Book I. that any two sides of a triangle are together greater than the third. This, however, is manifest without demonstration, if we adopt Archimedes's definición of a straight... ## general Report on Public Instruction in the lower Provinces of the Bengal ...

JOHN GRAY - 1857 - 784 pages
...each ? 5. If a : b : : c : d show that a + b : J : : c + d : d and that am : b" : : C" : d" EUCLID. 1. Any two sides of a triangle are together greater than the third side. the squares of the sides containing it by twice the rectangle contained by the side upon which, when... ## Middle-class education. 2

Middle-class education - 1857 - 70 pages
...line. What figure would be formed by placing two equilateral triangles base to base ? 81. Prove that any two sides of a triangle are together greater than the third side. Is the same proposition true of the angles of a triangle ? Give reasons for your answer. 32. Prove... ## National Society's Monthly Paper

1858 - 380 pages
...plane rectilineal angle, and show how to bisect one, that is, to divide it into two equal angles. 2. Any two sides of a triangle are together greater than the third side. Is the same proposition true of the angles of a triangle? 3. What is a parallelogram? Prove that the... ## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...difference. Let two circumferences cut each other in the point A. Draw the radii CA, DA ; then, because any two sides of a triangle are together greater than the third side (Prop. VIII., B. I.), CD must be less than the sum of AD and AC. Also, DA must be less than the sum... 