## Elements of Geometry and Trigonometry |

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Page 16

**Let**AB and DE be two straight A lines , intersecting each other at C ; then will the angle ECB be equal to the angle ...**Let**the triangle EDF , be placed upon the triangle BAC , so that the point E shall**fall**upon B , and the side ED on ... Page 17

DF is equal to AC ; therefore , the point F will

DF is equal to AC ; therefore , the point F will

**fall**on C , and the third side EF , will coincide with the third side BC ... E FB For to apply the one to the other ,**let**the side EF be placed on its equal BC , the point E**falling**on B ... Page 19

If the point G

If the point G

**fall**on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B Ꮐ Third Case . Lastly , if the point G**fall**within the triangle BAC ...**Let**the side ED = BA , the side EF BOOK I. 19. Page 22

Let A be the point , and DE the given line . A Let us suppose that we can draw two perpendiculars , AB , AC . ... If from a point without a straight line , a perpendicular be

Let A be the point , and DE the given line . A Let us suppose that we can draw two perpendiculars , AB , AC . ... If from a point without a straight line , a perpendicular be

**let fall**on the line , and oblique lines be drawn to ... Page 25

Let the two lines AC , BD , A be perpendicular to AB ; then will they be parallel . B For , if they could meet in a point O , on either side of AB , there would be two perpendiculars OA , OB ,

Let the two lines AC , BD , A be perpendicular to AB ; then will they be parallel . B For , if they could meet in a point O , on either side of AB , there would be two perpendiculars OA , OB ,

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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