## Elements of Geometry and Trigonometry |

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Page 17

**Hence**, the point D , falling at the same time in the two straight lines BA and CA , must fall at their intersection A :**hence**, the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . A Cor . Page 28

**Hence**AB and CD are . perpendicular to the same straight line ;**hence**they are parallel ( Prop . XVIII . ) . A R Q P T D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being CH ... Page 29

and since DG is parallel to AB , the angle DGC is equal to BAC ;

and since DG is parallel to AB , the angle DGC is equal to BAC ;

**hence**, the angle DEF is equal to BAC ( Ax . 1. ) . E G F Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC ... Page 31

right angles :

right angles :

**hence**, if all the angles of a quadrilateral are equal , each of them will be a right angle ; a conclusion which sanctions the seventeenth Definition , where the four angles of a quadrilateral are asserted to be right ... Page 32

and since AB , CD , are parallel , the angle ABD BDC :

and since AB , CD , are parallel , the angle ABD BDC :

**hence**the two triangles are equal ( Prop . VI . ) ; therefore the side AB , opposite the angle ADB , is equal to the side DC , opposite the equal angle DBC ; and the third sides AD ...### 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