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 62
... less than the squares of the sides containing that angle , by twice the rectangle contained by either of these sides , and the straight line intercepted between the perpendicular , let fall upon it from the opposite angle , and the ...
... less than the squares of the sides containing that angle , by twice the rectangle contained by either of these sides , and the straight line intercepted between the perpendicular , let fall upon it from the opposite angle , and the ...
Σελίδα 67
... . def . 1. ) Therefore the angle GDB is a right angle : But FDB is likewise a right angle ; wherefore the angle FDB is equal to the angle GDB , the greater A G F E to the less , which is impossible : Therefore G OF GEOMETRY . BOOK III . 67.
... . def . 1. ) Therefore the angle GDB is a right angle : But FDB is likewise a right angle ; wherefore the angle FDB is equal to the angle GDB , the greater A G F E to the less , which is impossible : Therefore G OF GEOMETRY . BOOK III . 67.
Σελίδα 69
... the angle FEB , the less to the greater , which is impossible therefore AC , BD do not bisect one another . Where- fore , if in a circle , & c . Q. E. D. PROP . V. THEOR . If two circles cut one OF GEOMETRY . BOOK III . 6.9.
... the angle FEB , the less to the greater , which is impossible therefore AC , BD do not bisect one another . Where- fore , if in a circle , & c . Q. E. D. PROP . V. THEOR . If two circles cut one OF GEOMETRY . BOOK III . 6.9.
Σελίδα 70
... less to the greater , which is im- possible therefore E is not the centre of the circles ABC , CDG . Wherefore , if two circles , & c . Q.E.D. PROP . VI . THEOR . F E If two circles touch one another internally , they cannot have the ...
... less to the greater , which is im- possible therefore E is not the centre of the circles ABC , CDG . Wherefore , if two circles , & c . Q.E.D. PROP . VI . THEOR . F E If two circles touch one another internally , they cannot have the ...
Σελίδα 72
... less than KD : And because MK , DK are drawn to the point K within the triangle MLD from M , D , the extremities of its side MD ; MK , KD are less ( 21. 1. ) than ML ; LD , whereof MK is equal to ML ; therefore the remainder DK is less ...
... less than KD : And because MK , DK are drawn to the point K within the triangle MLD from M , D , the extremities of its side MD ; MK , KD are less ( 21. 1. ) than ML ; LD , whereof MK is equal to ML ; therefore the remainder DK is less ...
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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