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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 84
... is proved as before . The joints between the arch - stones , or voussoirs , are only continuations of radii drawn from the centre O of the circle . MN B ELEMENTS OF GEOMETRY . BOOK IV . DEFINITIONS . 1 84 ELEMENTS , & c .
... is proved as before . The joints between the arch - stones , or voussoirs , are only continuations of radii drawn from the centre O of the circle . MN B ELEMENTS OF GEOMETRY . BOOK IV . DEFINITIONS . 1 84 ELEMENTS , & c .
Página 85
... DEFINITIONS . 1 A RECTILINEAL figure is said to be inscribed in another rectilineal figure , when all the angles of the inscribed figure are upon the sides of the figure in which it is inscribed , each upon each . 2. In like manner , a ...
... DEFINITIONS . 1 A RECTILINEAL figure is said to be inscribed in another rectilineal figure , when all the angles of the inscribed figure are upon the sides of the figure in which it is inscribed , each upon each . 2. In like manner , a ...
Página 101
... definition , the multiple of the first is greater than that of the second , but the multiple of the third is not ... definition A has to D the ratio compounded of the ratios of A to B , B to C , C to D ; A may also be said to have to D ...
... definition , the multiple of the first is greater than that of the second , but the multiple of the third is not ... definition A has to D the ratio compounded of the ratios of A to B , B to C , C to D ; A may also be said to have to D ...
Página 102
... definition , the ratio " of A to C is compounded of the ratios of A to B , and B to C , a ratio , " which is compounded of two equal ratios , is duplicate of either of " these ratios . " 12. If four magnitudes are continual ...
... definition , the ratio " of A to C is compounded of the ratios of A to B , and B to C , a ratio , " which is compounded of two equal ratios , is duplicate of either of " these ratios . " 12. If four magnitudes are continual ...
Página 103
... definition ; whence this is called ordinate proportion . It is demonstrated in the 22d Prop . Book 5 . 21. Ex æquali , in proportione perturbata , seu inordinata : from equality , in perturbate , or disorderly proportion ; this term is ...
... definition ; whence this is called ordinate proportion . It is demonstrated in the 22d Prop . Book 5 . 21. Ex æquali , in proportione perturbata , seu inordinata : from equality , in perturbate , or disorderly proportion ; this term is ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore