## Elements of Geometry and Trigonometry |

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Page 12

The

The

**common**name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions .. A scholium is a remark on one or several preceding ... Page 14

B Let A and B be the two

B Let A and B be the two

**common**points . 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 ) . Page 15

which can only be the case when the lines CD and CE coincide : therefore , the straight lines which have two points A and B

which can only be the case when the lines CD and CE coincide : therefore , the straight lines which have two points A and B

**common**, cannot separate at any point , when produced ; hence they form one and the same straight line . Page 16

Take away from both , the

Take away from both , the

**common**angle ACE , there remains the angle ACD , equal to its opposite or vertical angle ECB ( Ax . 3. ) . Scholium . The four angles formed about a point by two straight lines , which intersect each other ... Page 20

Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , B by hypothesis ; AD is

Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , B by hypothesis ; AD is

**common**, and BD is equal to DC by construction : therefore , by the last ...### 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