Elements of geometry, based on Euclid, book i1877 |
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Page 10
... describe an equilateral triangle on a given finite straight line . Let AB be the given straight line . It is required to describe an equilateral triangle on AB . C A B E CONSTRUCTION . - From the centre A , at the distance AB , describe ...
... describe an equilateral triangle on a given finite straight line . Let AB be the given straight line . It is required to describe an equilateral triangle on AB . C A B E CONSTRUCTION . - From the centre A , at the distance AB , describe ...
Page 11
... describe the equilateral triangle DAB ( Book I. , A DAB e- Prop . 1 ) . Produce the straight lines DA , DB , to E and F ( Post . 2 ) . From the centre B , at the dis- tance BC , describe the circle CGH , meeting DF in G ( Post . 3 ) ...
... describe the equilateral triangle DAB ( Book I. , A DAB e- Prop . 1 ) . Produce the straight lines DA , DB , to E and F ( Post . 2 ) . From the centre B , at the dis- tance BC , describe the circle CGH , meeting DF in G ( Post . 3 ) ...
Page 12
... describe the circle DEF , cutting AB in E ( Post . 3 ) . Then AE shall be equal to C. PROOF . - Because the point A is the centre of the circle AE = AD . DEF , AE is equal to AD ( Def . 15 ) . AD = C . AE and C each = AD . .. AE = C ...
... describe the circle DEF , cutting AB in E ( Post . 3 ) . Then AE shall be equal to C. PROOF . - Because the point A is the centre of the circle AE = AD . DEF , AE is equal to AD ( Def . 15 ) . AD = C . AE and C each = AD . .. AE = C ...
Page 19
... describe the equilateral triangle ABC ( I. 1 ) . Bisect the angle ACB by the straight line CD ( I. 9 ) . Then AB shall be cut into two equal parts in the point D. PROOF . - Because AC is equal to CB A C D B ( Const . ) , and CD common ...
... describe the equilateral triangle ABC ( I. 1 ) . Bisect the angle ACB by the straight line CD ( I. 9 ) . Then AB shall be cut into two equal parts in the point D. PROOF . - Because AC is equal to CB A C D B ( Const . ) , and CD common ...
Page 20
... describe the circle EGF , meet- ing AB in F and G ( Post . 3 ) . Bisect FG in H ( I. 10 ) . Join CF , CH , CG . Then CH shall be perpendicular to AB . PROOF . Because FH is equal to HG Const . ) , and HC common to the two triangles FHC ...
... describe the circle EGF , meet- ing AB in F and G ( Post . 3 ) . Bisect FG in H ( I. 10 ) . Join CF , CH , CG . Then CH shall be perpendicular to AB . PROOF . Because FH is equal to HG Const . ) , and HC common to the two triangles FHC ...
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Common terms and phrases
ABC is equal alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles BGH angles CBA angles equal APPLIED base BC bisect centre cloth coincide common Const CONSTRUCTION describe diagonal Divide double draw equal to BC exterior angle extremity Fcap figure given point given straight line Glasgow gram greater half Illustrated interior and opposite isosceles triangle join length less Let ABC LL.D London Maps meet opposite angles opposite sides parallel parallel to BC parallelogram parallelogram ABCD perpendicular Plates Post 8vo produced Professor PROOF PROOF.-Because proved Q. E. D. Proposition respectively right angles right angles Ax School Science shown side BC sides square things triangle ABC triangle DEF whole
Popular passages
Page 23 - 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 33 - 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 43 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Page 15 - 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 11 - 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 37 - 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 41 - ... together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 15 - 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 55 - 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 24 - 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.