## Elements of Geometry |

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Page iv

Also an improved demonstration of the

Also an improved demonstration of the

**theorem**for the solidity of the triangular pyramid , by M. Queret of St. Malo , is subjoined at the end . But the principal improvement in this edition consists in a new demonstration of the**theorem**... Page 3

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A

**Theorem**is a truth which becomes evident by a process of reasoning called a demonstration . A Problem is a question proposed which requires a solution . A Lemma is a subsidiary truth employed in the demonstration of a**theorem**, or in ... Page 4

**THEOREM**. > > 27. All right angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF ... Page 5

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**THEOREM**. 32. Two straight lines , which have two points common , coincide throughout , and form one and the same straight line . Demonstration . Let the two points , which are common to the two lines , be A and B ( fig . 19 ) . Page 6

**THEOREM**. Fig . 2 ) 33. If two adjacent angles ACD , DCB ( fig . 20 ) , are together equal to two right angles , the two exterior sides AC , CB , are in the same straight line . Demonstration . For if CB is not the line AC produced ...### What people are saying - Write a review

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### Common terms and phrases

ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex vertices whence