## Elements of Geometry and Trigonometry |

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Page 20

... if the angle D were less than A , it would

... if the angle D were less than A , it would

**follow**, that the side EF must be less than BC : but EF is equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it . Page 21

For , if the angle C < B , it

For , if the angle C < B , it

**follows**, from what has just been proved , that AB < AC ; which is contrary to the hypothesis . It the angle CB , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition . Page 22

from whence it

from whence it

**follows**, that between the same two points , A and F , two straight lines can be drawn , which is impossible ( Ax . 11. ) : hence , two perpendiculars cannot be drawn from the same point to the same ... Page 32

... is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the opposite sides of a parallelogram are equal . - Again , since the triangles are equal , it

... is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the opposite sides of a parallelogram are equal . - Again , since the triangles are equal , it

**follows**that the angle A is ... Page 33

In the case of the rhombus , the sides AB , BC , being equal , the triangles AEB , EBC , have all the sides of the one equal to the corresponding sides of the other , and are therefore equal : whence it

In the case of the rhombus , the sides AB , BC , being equal , the triangles AEB , EBC , have all the sides of the one equal to the corresponding sides of the other , and are therefore equal : whence it

**follows**that the angles AEB ...### 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