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" AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. "
A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well ... - Page 257
by Charles Hutton - 1818
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 244 pages
...make the opposite vertical angles equal, each alternate pair of lines will be in the same st. line. 3. The difference of any two sides of a triangle is less than the remaining side. 4. Each angle of an equilateral triangle is equal to one-third of two right angles,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 252 pages
...Book V. has been studied. GEOMETRICAL EXERCISES ON BOOK I. THEOREMS. Prop. 1 . The difference between any two sides of a triangle is less than the third side. Prop. 2- The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can...
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A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - Examinations - 1859 - 352 pages
...is half a right angle. 9. Divide a right angle into three equal angles. 10. The difference between any two sides of a triangle is less than the third side. 11. On a given line describe a square of which the given line shall be the diagonal. 12. The diagonals...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 142 pages
...CAO (I. 8), and the line AO bisects the angle BAC. EXERCISE Vill.— THEOREM. The difference between two sides of a triangle is less than the third side. Let ABC be a triangle ; then the differ- C ence between any two of its sides, as AB and AC, is less than the third side BC. For...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...however near the point A may be to the line BC. It may be easily shewn from this proposition, that the difference of any two sides of a triangle is less than the third side. Prop. xxn. When the sum of two of the lines is equal to, and when it is less than, the third line;...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - Mathematics - 1860 - 1022 pages
...distance between two points, is a single right lie* drew* from ilio one point to the other. THEOREM XI. Let ABC be a triangle; then will the difference of any two sides, aŤ AB — AC, be less than the third side BC. For, produce the less side AC to D, till AD be equal...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1860 - 246 pages
...Book V. has been studied. GEOMETRICAL EXERCISES ON BOOK I. THEOREMS. Prop. 1. The difference between any two sides of a triangle is less than the third side. Prop. 2. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can...
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The Modern Mechanic: A Scientific and Calculator, Comprising Rules and ...

William Grier - Mechanical engineering - 1861 - 316 pages
...two of its sides be greater than the third side ; as, for instance, AC + CB greater than AB. 1 1 . Let ABC be a triangle ; then will the difference of...two sides, as AB — AC, be less than the third side BC. 12. Let the line EF cut the two parallel lines AB, CD ; then will the angle AEF be equal to the...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...the perpendicular. 17. Prove I. 20, without producing any side, by bisecting one of the angles. 18. The difference of any two sides of a triangle is less than the third side. 19. If from any point within a triangle straight lines be drawn to the vertices of the three angles,...
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Conic Sections and Analytical Geometry: Theoretically and Practically ...

Horatio Nelson Robinson - Conic sections - 1862 - 356 pages
...and Because EF is equal to EG we have EF'—EF=EF'—EG. But JEF— J00, is less than JF'ff, because the difference of any two sides of a triangle is less than the third side. That is, EF' — EF is less than A' A; consequently the point E is without the curve (Prop. 2), and...
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