## Elements of Geometry and Trigonometry |

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Page 45

But two points are sufficient to

But two points are sufficient to

**determine**the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . Page 58

and since two points

and since two points

**determine**a line , AD is that perpendicular . Scholium . The same construction serves for making a right angle BAD , at a given point A , on a given straight line BC . PROBLEM III . From a given point , without a ... Page 85

When the homologous sides are

When the homologous sides are

**determined**, it is easy to form the proportions : AB : DC : AC : DE :: BC : CE . PROPOSITION XIX . THEOREM . Two triangles , which have their homologous sides proportional , are equiangular and similar . Page 108

tinue diminishing , and would soon elude our comparisons by their minuteness , this would be but an imperfect mechanical method , from which G no conclusion could be obtained to

tinue diminishing , and would soon elude our comparisons by their minuteness , this would be but an imperfect mechanical method , from which G no conclusion could be obtained to

**determine**whether the lines AC , CB , have or have not a ... Page 109

The angle of a regular polygon , like the angle of an equiangular polygon , is

The angle of a regular polygon , like the angle of an equiangular polygon , is

**determined**by the number of its sides ( Book I. Prop . XXVI . ) . PROPOSITION II . THEOREM . Any regular polygon may be BOOK V. 109 BOOK I BOOK V Regular ...### 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