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 |
Dentro del libro
Página 32
... manner , it may be de- monstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. B PROP . XVIII . THEOR . C D. The greater side of every triangle has the greater ...
... manner , it may be de- monstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. B PROP . XVIII . THEOR . C D. The greater side of every triangle has the greater ...
Página 33
... BC . In the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. E PROP . XXI . THEOR . If from the ends OF GEOMETRY . BOOK I. 333.
... BC . In the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. E PROP . XXI . THEOR . If from the ends OF GEOMETRY . BOOK I. 333.
Página 39
... manner it may be demonstrated that they do not meet towards A , C ; but those straight lines . which meet neither way , ( 30. Def . ) to one another . fore , if a straight line & c . C F though produced ever so far , are parallel AB ...
... manner it may be demonstrated that they do not meet towards A , C ; but those straight lines . which meet neither way , ( 30. Def . ) to one another . fore , if a straight line & c . C F though produced ever so far , are parallel AB ...
Página 46
... manner , it may be demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E. D .. B PROP . XL . THEOR . Equal triangles on the 46 ' ELEMENTS T.
... manner , it may be demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E. D .. B PROP . XL . THEOR . Equal triangles on the 46 ' ELEMENTS T.
Página 47
... manner it may be demonstrated that there is no other parallel to it but AD ; AD is therefore parallel to BF . Wherefore equal triangles , & c . Q. E. D. PROP . XLI . THEOR . If a parallelogram and a triangle be upon the same base , and ...
... manner it may be demonstrated that there is no other parallel to it but AD ; AD is therefore parallel to BF . Wherefore equal triangles , & c . Q. E. D. PROP . XLI . THEOR . If a parallelogram and a triangle be upon the same base , and ...
Otras ediciones - Ver todas
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