## Elements of geometry, based on Euclid, book i |

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ABC is equal alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles BGH angles CBE angles equal APPLIED base BC bisect centre cloth coincide common Const CONSTRUCTION describe diagonal Divide double draw equal sides equal to AC exterior angle extremity Fcap figure given point given straight line Glasgow gram greater Illustrated interior and opposite isosceles triangle join length less Let ABC LL.D London Maps meet opposite angles opposite sides parallel parallel to CD parallelogram parallelogram ABCD perpendicular Plates Post 8vo Problem produced Professor PROOF PROOF.—Because Proposition proved respectively right angles right angles Ax School Science shown side BC sides square things triangle ABC triangle DEF whole

### Popular passages

Page 21 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Page 31 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.

Page 41 - Parallelograms upon the same base, and between the same parallels, are equal to one another.

Page 13 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall also be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC...

Page 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.

Page 35 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Page 39 - ... together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 13 - J which the equal sides are opposite, shall be equal, each to each, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.

Page 53 - IF the square described upon one of 'the sides of a triangle be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Page 22 - If, at a point in a straight line, two other straight lines, on the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.