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 TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 14
... fore the angles ABC , BCA are less than two right angles . In like man- ner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . B PROP . XI . THEOR . D The greater side of every triangle has ...
... fore the angles ABC , BCA are less than two right angles . In like man- ner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . B PROP . XI . THEOR . D The greater side of every triangle has ...
Página 24
... fore all the interior , together with all the exterior angles of the figure , are equal to twice as many right angles as there are sides of the figure ; that is , they are equal to all the interior angles of the figure , together with ...
... fore all the interior , together with all the exterior angles of the figure , are equal to twice as many right angles as there are sides of the figure ; that is , they are equal to all the interior angles of the figure , together with ...
Página 28
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 29. 1. ) to DBCF , because they are upon the same base BC , and between the same pa- E A D F B rallels BC , EF ; but the triangle ABC is the half of the ...
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 29. 1. ) to DBCF , because they are upon the same base BC , and between the same pa- E A D F B rallels BC , EF ; but the triangle ABC is the half of the ...
Página 31
... fore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described upon the straight line BC , and the squares GB , HC upon BA , AC : wherefore the square upon the side BC is equal to the squares upon ...
... fore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described upon the straight line BC , and the squares GB , HC upon BA , AC : wherefore the square upon the side BC is equal to the squares upon ...
Página 32
... fore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another ( 1. Ax . ) ; therefore CA is equal to CB ; wherefore , CA , AB , CB are equal to one another ; and the triangle ABC is ...
... fore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another ( 1. Ax . ) ; therefore CA is equal to CB ; wherefore , CA , AB , CB are equal to one another ; and the triangle ABC is ...
Otras ediciones - Ver todas
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
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 draw Prob 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