## Elements of Geometry and Trigonometry |

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Page 16

E D FB A For , these triangles may be so applied to each other , that they shall exactly coincide . Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall

E D FB A For , these triangles may be so applied to each other , that they shall exactly coincide . Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall

**fall**upon B , and the side ED on the equal side BA ... 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 ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor . Page 19

Now , there may be three cases in the proposition , according as the point G

Now , there may be three cases in the proposition , according as the point G

**falls**without the triangle ABC , or upon ... 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. ) ... Page 22

If from a point without a straight line , a perpendicular be let

If from a point without a straight line , a perpendicular be let

**fall**on the line , and oblique lines be drawn to different points : 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on ... Page 25

For , if they could meet in a point Q , on either side of AB , there would be two per- B D pendiculars OA , OB , let

For , if they could meet in a point Q , on either side of AB , there would be two per- B D pendiculars OA , OB , let

**fall**from the same point on the same straight line ; which is impossible ( Prop . XIV . ) . PROPOSITION XIX . THEOREM .### 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 construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole