## 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 AD2 to each , and observing that the right angled trian- gles ABD , ADC ,

Adding AD2 to each , and observing that the right angled trian- gles ABD , ADC ,

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

consequently the triangle ABC

consequently the triangle ABC

**gives**AB2 + BC - 2AE2 + 2BE2 . The triangle ADC**gives**, in like manner . AD2 + DC2-2AE2 + 2DE2 . Adding the corresponding members together , and observing that BE and DE are equal , we shall have AB2 + AD + ... 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 E A F H same manner , that EG : FH :: GB : HD , and so on ; hence the lines AB , CD , are cut proportionally by the ...### 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