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 vii
... third Book , the remarks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the elements of the science . The 27th , 28th and ...
... third Book , the remarks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the elements of the science . The 27th , 28th and ...
Page ix
... Third Book , I have departed from EUCLID altoge- ther , with a view of rendering it both shorter and more comprehenfive . This , however , is not attempted by introducing a mode of reafon- ing lefs rigorous than that of the Greek geome ...
... Third Book , I have departed from EUCLID altoge- ther , with a view of rendering it both shorter and more comprehenfive . This , however , is not attempted by introducing a mode of reafon- ing lefs rigorous than that of the Greek geome ...
Page xiv
... third ; it may be replied , that this is no doubt a truth , which , without proof , moft men will be inclined to admit ; but , are we for that reafon to account it of no confequence to know what the propofitions are , which muft cease ...
... third ; it may be replied , that this is no doubt a truth , which , without proof , moft men will be inclined to admit ; but , are we for that reafon to account it of no confequence to know what the propofitions are , which muft cease ...
Page xv
... third , neither could it be true , that the great- er fide of every triangle is oppofite to the greater angle , nor that the equal fides are oppofite to equal angles , nor , laftly , that things equal to the fame thing are equal to one ...
... third , neither could it be true , that the great- er fide of every triangle is oppofite to the greater angle , nor that the equal fides are oppofite to equal angles , nor , laftly , that things equal to the fame thing are equal to one ...
Page 10
... third fides , shall be equal ; and the two triangles fhall be equal ; and their other angles fhall be equal , each to each , viz . thofe to which the equal fides are oppofite . Let ABC , DEF be two triangles which have the two fides AB ...
... third fides , shall be equal ; and the two triangles fhall be equal ; and their other angles fhall be equal , each to each , viz . thofe to which the equal fides are oppofite . Let ABC , DEF be two triangles which have the two fides AB ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 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...
Page 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.
Page 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...
Page 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...
Page 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.
Page 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...
Page 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.