## Elements of Geometry and Trigonometry |

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Page 32

B Let

B Let

**ABCD**be a parallelogram : then will D AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The triangles ABD , DBC , have a common side BD ; and since AD , BC , are parallel , they have also the angle ADB = DBC ... Page 33

For a like reason AB is parallel to CD : therefore the quadrilateral

For a like reason AB is parallel to CD : therefore the quadrilateral

**ABCD**is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and ... Page 55

The opposite angles A and C , of an inscribed quadrilateral

The opposite angles A and C , of an inscribed quadrilateral

**ABCD**, are together equal to two right angles : for the anΑΙ gle BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD ... Page 69

B A B Let AB be the common base of D CF E DE CE the two parallelograms

B A B Let AB be the common base of D CF E DE CE the two parallelograms

**ABCD**, ABEF : and since they are supposed to have the same altitude , A their upper bases DC , FE , will be both situated in one straight line parallel to AB . Page 70

Hence these two parallelograms

Hence these two parallelograms

**ABCD**, ABEF , which have the same base and altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM .### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude angled triangle base become Book called centre chord circle circumference circumscribed common cone consequently contained corresponding 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 logarithm manner means measured meet middle multiplied number of sides 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 sides similar sine solid solid angle sphere spherical triangle square straight line suppose taken tang tangent THEOREM third triangle triangle ABC unit vertex whole

### Popular passages

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Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.