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 páginas |
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Página 30
... things that are equal to the same are equal ( 1. Ax . ) to one another ; therefore the angles CBE , EBD are equal to the an- gles DBA , ABC ; but CBE , EBD , are two right angles ; therefore DBA , ABC are together equal to two right ...
... things that are equal to the same are equal ( 1. Ax . ) to one another ; therefore the angles CBE , EBD are equal to the an- gles DBA , ABC ; but CBE , EBD , are two right angles ; therefore DBA , ABC are together equal to two right ...
Página 46
... things are equal . ( 7. Ax . ) ; therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c . Q. E. D. PROP . XXVIII . THEOR . Triangles upon equal bases , and between the same parallels , are equal to one ...
... things are equal . ( 7. Ax . ) ; therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c . Q. E. D. PROP . XXVIII . THEOR . Triangles upon equal bases , and between the same parallels , are equal to one ...
Página 53
... things between which it is placed " are equal to one another . " II . A E In every parallelogram , any of the parallelograms about a di- ameter , together with the two complements , is called a Gno- mon . " Thus the parallelo- " gram HG ...
... things between which it is placed " are equal to one another . " II . A E In every parallelogram , any of the parallelograms about a di- ameter , together with the two complements , is called a Gno- mon . " Thus the parallelo- " gram HG ...
Página 94
... thing required is done ; for in the circle ABC a straight line BC is placed equal to D : But , if it is not , BC is greater than D ; make CE equal ( 3. 1. ) to D , and from the centre C , at the distance CE , describe the circle AEF ...
... thing required is done ; for in the circle ABC a straight line BC is placed equal to D : But , if it is not , BC is greater than D ; make CE equal ( 3. 1. ) to D , and from the centre C , at the distance CE , describe the circle AEF ...
Página 109
... things being supposed , if M has to N the same ratio which A has to D , then , for shortness ' sake , M is said to have to N a ratio compounded of the same ratios , which compound the ratio of A to D ; that is , a ratio compounded of ...
... things being supposed , if M has to N the same ratio which A has to D , then , for shortness ' sake , M is said to have to N a ratio compounded of the same ratios , which compound the ratio of A to D ; that is , a ratio compounded of ...
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Términos y frases comunes
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