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 σελίδες |
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Σελίδα viii
... reason , because , to mea- sure the length of the simplest of all the curves which Geometry treats of , and the space contained within it , are problems that certainly belong to the elements of the science , especially as they are not ...
... reason , because , to mea- sure the length of the simplest of all the curves which Geometry treats of , and the space contained within it , are problems that certainly belong to the elements of the science , especially as they are not ...
Σελίδα xii
... reasons , I would willingly reserve it , or rather a compend of it , for a separate work , intended as an introduction to the study of that analysis . In explaining the elements of Plane and Spherical Trigonometry , xii PRFACE .
... reasons , I would willingly reserve it , or rather a compend of it , for a separate work , intended as an introduction to the study of that analysis . In explaining the elements of Plane and Spherical Trigonometry , xii PRFACE .
Σελίδα xv
... reason to account it of no consequence to know what the propositions are , which must cease to be true if this proposition were sup- posed to be false ? Is it not useful to know , that unless it be true , that any two sides of a ...
... reason to account it of no consequence to know what the propositions are , which must cease to be true if this proposition were sup- posed to be false ? Is it not useful to know , that unless it be true , that any two sides of a ...
Σελίδα 34
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Σελίδα 44
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder , AE is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; now AB is also equal to DC ; therefore ...
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder , AE is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; now AB is also equal to DC ; therefore ...
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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