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 xiv
... thing that admits of being proved . Indeed those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition ...
... thing that admits of being proved . Indeed those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition ...
Página xv
... things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that which we receive from EUCLID's demon- stration . To all this it may be added , that ...
... things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that which we receive from EUCLID's demon- stration . To all this it may be added , that ...
Página 21
... Things which are doubles of the same thing , are equal to one another VII . Things which are halves of the same thing , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same ...
... Things which are doubles of the same thing , are equal to one another VII . Things which are halves of the same thing , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same ...
Página 22
... things which are equal to the same are equal to one another , ( 1 . Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the ...
... things which are equal to the same are equal to one another , ( 1 . Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the ...
Página 23
... things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be ...
... things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be ...
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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