Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 80
... ABCD be a circle , and BAD , BED angles in the same segment BAED : The angles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And . first , let the segment BAED be great- er than a semicircle , and join BF ...
... ABCD be a circle , and BAD , BED angles in the same segment BAED : The angles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And . first , let the segment BAED be great- er than a semicircle , and join BF ...
Σελίδα 81
... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles . D Join AC , BD . The angle CAB is equal ( 21. 3. ) to the angle CDB , because they are in the same seg- ment ...
... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles . D Join AC , BD . The angle CAB is equal ( 21. 3. ) to the angle CDB , because they are in the same seg- ment ...
Σελίδα 86
... ABCD be a circle , of which the diameter is BC , and centre E ; draw CA dividing the circle into the segments ABC , ADC , and join BB , AD , DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC ...
... ABCD be a circle , of which the diameter is BC , and centre E ; draw CA dividing the circle into the segments ABC , ADC , and join BB , AD , DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC ...
Σελίδα 87
... ABCD is a quadrilateral figure in a circle , any two of its opposite angles are equal ( 22. 3. ) to two right angles ; there- fore the angles ABC , ADC are equal to two right angles ; and ABC is less than a right angle ; wherefore the ...
... ABCD is a quadrilateral figure in a circle , any two of its opposite angles are equal ( 22. 3. ) to two right angles ; there- fore the angles ABC , ADC are equal to two right angles ; and ABC is less than a right angle ; wherefore the ...
Σελίδα 89
... ABCD , cut one another in the point E : the rectangle contained by AE , EC is equal to the rectangle contained by BE , ED . If AC , BD pass , each of them through the centre , so that E is the centre , it is evident , that AE , EC , BE ...
... ABCD , cut one another in the point E : the rectangle contained by AE , EC is equal to the rectangle contained by BE , ED . If AC , BD pass , each of them through the centre , so that E is the centre , it is evident , that AE , EC , BE ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore