## Elements of Geometry and Trigonometry |

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Page 72

This product will

This product will

**give**the number of superficial units in the surface ; because , for one unit in height , there are as many superficial units as there are linear units in the base ; for two units in height twice as many ; for three ... Page 76

... the difference , AC - AB must be equal to the difference AE - AF , which

... the difference , AC - AB must be equal to the difference AE - AF , which

**gives**BC = EF ; but IG is equal to BC , and DG to EF , since the lines are parallel ; therefore IGDH is equal to a square described on BC . Page 80

Adding AD to each , and observing that the right angled triangles ABD , ADC ,

Adding AD to each , and observing that the right angled triangles ABD , ADC ,

**give**AD + BD2 = AB2 , and AD2 + CD2 = AC2 , we have AB2 = BC2 + AC2-2BC × CD . Secondly . When the perpendicular AD falls without the triangle ABC , we have ... Page 81

consequently the triangle ABC

consequently the triangle ABC

**gives**AB2 + BC2-2AE2 + 2BE2 . The triangle ADC**gives**, in like manner . AD2 + DC2-2AE2 + 2DE2 . E 1 Adding the corresponding members together , and observing that BE and DE are equal , we shall have AB2 + ... Page 82

And by reason of the common ratio OE : OF , those two proportions

And by reason of the common ratio OE : OF , those two proportions

**give**AE CF B :: EG : FH . It may be proved in the same manner , that EG : FH :: GB : HD , and so on : hence the lines AB , CD , are cut proportionally by the para is AC ...### 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