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 TrigonometryBell & Bradfute, 1804 - 440 páginas |
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Resultados 6-10 de 64
Página 13
... then is the angle BDC greater than the angle BCD . A. gain , becaufe CB is equal to DB , st A B. the angle BDC is equal to the angle BCD ; but BDC has a 5. 1 . been Book I. been proved to be greater than the fame OF GEOMETRY .. 13.
... then is the angle BDC greater than the angle BCD . A. gain , becaufe CB is equal to DB , st A B. the angle BDC is equal to the angle BCD ; but BDC has a 5. 1 . been Book I. been proved to be greater than the fame OF GEOMETRY .. 13.
Página 14
... proved to be greater than the fame BCD ; which is im- poffible . The cafe in which the vertex of one triangle is up- on a fide of the other , needs no demonstration . Therefore , upon the fame base , and on the fame side of it , there ...
... proved to be greater than the fame BCD ; which is im- poffible . The cafe in which the vertex of one triangle is up- on a fide of the other , needs no demonstration . Therefore , upon the fame base , and on the fame side of it , there ...
Página 31
... proved to be equal to GHD ; there- c 15. 1 . fore EGB is likewise equal to GHD ; add to each of these the angle - BGH ; therefore the angles EGB , BGH are equal to the angles BGH , GHD ; but EGB , BGH are equal to d 13. I , two right ...
... proved to be equal to GHD ; there- c 15. 1 . fore EGB is likewise equal to GHD ; add to each of these the angle - BGH ; therefore the angles EGB , BGH are equal to the angles BGH , GHD ; but EGB , BGH are equal to d 13. I , two right ...
Página 100
... proved equal to BAD : therefore the remaining angle DBE is equal to the angle BCD in the alternate segment of the circle . Wherefore , if a straight line , & c . Q. E. D. A 10. I. UPO PROP . XXXIII . PROB . PON a given ftraight line to ...
... proved equal to BAD : therefore the remaining angle DBE is equal to the angle BCD in the alternate segment of the circle . Wherefore , if a straight line , & c . Q. E. D. A 10. I. UPO PROP . XXXIII . PROB . PON a given ftraight line to ...
Página 141
... proved , A : Č :: B : C , and inverfely c , C : A :: C : B. Therefore , c A. 5 . & c . Q.E. D. Ο PROP . VIII . THEOR . unequal magnitudes , the greater has a great- er ratio to the fame than the lefs has ; and the fame magnitude has a ...
... proved , A : Č :: B : C , and inverfely c , C : A :: C : B. Therefore , c A. 5 . & c . Q.E. D. Ο PROP . VIII . THEOR . unequal magnitudes , the greater has a great- er ratio to the fame than the lefs has ; and the fame magnitude has a ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Sin vista previa disponible - 2016 |
Términos y frases comunes
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifected Book cafe centre circle ABC circumference co-fine cof BC cylinder defcribed demonftrated diameter draw drawn equal angles equiangular equilateral polygon equimultiples Euclid exterior angle faid fame altitude fame manner fame plane fame ratio fame reaſon fecond fection fegment femicircle fhall fhewn fide BC fides fince firft firſt folid fore fquare fuch given ftraight line greater infcribed interfect join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals Q. E. D. PROP radius reafon rectangle contained rectilineal figure remaining angle ſpherical triangle ſquare tangent THEOR theſe thofe thoſe triangle ABC uſe wherefore
Pasajes populares
Página 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 84 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Página 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Página 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...
Página 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Página 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.
Página 54 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Página 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.