## Elements of Geometry and Trigonometry |

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Page 14

The sum of all the successive angles , BAC , CAD , DAE , EAF , formed on the same side of the straight line BF , is equal to two right angles ; for their sum is equal to that of the two adjacent an- ,

The sum of all the successive angles , BAC , CAD , DAE , EAF , formed on the same side of the straight line BF , is equal to two right angles ; for their sum is equal to that of the two adjacent an- ,

**gles**, BAC , CAF . Page 26

0 1 I Let the parallels AB , CD , be met by the secant line FE : then will ÖGB + GOD , or OGA + GOC , be equal to two right an- A

0 1 I Let the parallels AB , CD , be met by the secant line FE : then will ÖGB + GOD , or OGA + GOC , be equal to two right an- A

**gles**. E Alternate angles lie within the parallels , and on different sides of the secant line : AGO ... Page 70

... which have equal bases and altitudes , are equivalent , being halves of equivalent parallelograms . Two rectangles having the same altitude , are to each other as their bases . Let ABCD , AEFD , be two rectan- D

... which have equal bases and altitudes , are equivalent , being halves of equivalent parallelograms . Two rectangles having the same altitude , are to each other as their bases . Let ABCD , AEFD , be two rectan- D

**gles**70 GEOMETRY . Page 71

Let ABCD , AEFD , be two rectan- D

Let ABCD , AEFD , be two rectan- D

**gles**having the common altitude AD : they are to each other as their bases . AB , AE . A E Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 ... Page 91

Let ABC , DEF , be two similar triangles , having the angle A equal to D , and the angle B - E . Then , first , by reason of the equal an- G

Let ABC , DEF , be two similar triangles , having the angle A equal to D , and the angle B - E . Then , first , by reason of the equal an- G

**gles**A and D , according to the last proposition , we shall have ABC DEF :: AB.AC : DE.DF.### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole