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 Trigonometry |
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Page ix
... 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 cer- tainly 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 cer- tainly belong to the elements of the science , especially as they are not ...
Page xiii
... reasons , I would willingly reserve it , or rather a compend of it , for a separate work , intended as an in- troduction to the study of that analysis . In explaining the elements of Plane and Spherical Trigonometry , there is not much ...
... reasons , I would willingly reserve it , or rather a compend of it , for a separate work , intended as an in- troduction to the study of that analysis . In explaining the elements of Plane and Spherical Trigonometry , there is not much ...
Page xv
... reason to account it of no consequence to know what the propo- sitions are , which must cease to be true if this proposition were supposed 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 propo- sitions are , which must cease to be true if this proposition were supposed to be false ? Is it not useful to know , that unless it be true , that any two sides of a ...
Page 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 ...
Page 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 the ...
... 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 the ...
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Common terms and phrases
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 and similar 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 opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB proportional 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 parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY square straight line AC THEOR third touches the circle triangle ABC wherefore
Popular passages
Page 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 41 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Page 36 - If two triangles have two sides of the one equal to two sides of the...
Page 33 - ANY two sides of a triangle are together greater than the third side.
Page 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 308 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 25 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Page 56 - 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, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Page 18 - 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.
Page 90 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.