## Elements of Geometry and Trigonometry |

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Page 12

An axiom is a self -

An axiom is a self -

**evident**proposition . A theorem is a truth , which becomes**evident**by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . Page 14

In the first place it is

In the first place it is

**evident**that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Ax . 11. ) . Sup- A B pose , however , that on being ... Page 19

If the point G fall on the side BC , it is

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. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem ... Page 27

... CD , are not parallel , and will therefore mect if sufficiently produced . Cor . It is

... CD , are not parallel , and will therefore mect if sufficiently produced . Cor . It is

**evident**that the two lines IH BOOK I. 27. Page 28

It is

It is

**evident**that the two lines IH , CD , will meet on that side of EF on which the sum of the two angles OGH , GOD , is less than two right angles . PROPOSITION XXII . THEOREM . Two straight lines which are parallel to a third line ...### 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