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 sider |
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Resultater 1-5 af 24
Side 130
... multiple of B by m . When the number is intended to muf- tiply two or more magnitudes that follow , it is written thus , m.A + B . which fignifies the fum of A and B taken m times ; m.A — B is m times the excefs of A above B. Also ...
... multiple of B by m . When the number is intended to muf- tiply two or more magnitudes that follow , it is written thus , m.A + B . which fignifies the fum of A and B taken m times ; m.A — B is m times the excefs of A above B. Also ...
Side 131
... multiple of the firft is greater than the multiple of the fecond , equal to it , or lefs , the multiple of the third is also greater than the multiple of the fourth , equal to it , or lefs ; then the first of the magnitudes is faid to ...
... multiple of the firft is greater than the multiple of the fecond , equal to it , or lefs , the multiple of the third is also greater than the multiple of the fourth , equal to it , or lefs ; then the first of the magnitudes is faid to ...
Side 135
... multiple of a greater magnitude is greater than the fame multiple of a lefs . IV . That magnitude of which a multiple is greater than the fame multiple of another , is greater than that other magnitude . PROP . K 4 Book V. PROP . I ...
... multiple of a greater magnitude is greater than the fame multiple of a lefs . IV . That magnitude of which a multiple is greater than the fame multiple of another , is greater than that other magnitude . PROP . K 4 Book V. PROP . I ...
Side 136
... multiple of D + E + F . Therefore , & c . Q. E. D. COR . Hence , if m be any number , mD + mE + mF m.D + E + F . For mD , mE , and mF are multiples of D , E , and F by m , therefore their fum is also a multiple of D + E + F by m . I ...
... multiple of D + E + F . Therefore , & c . Q. E. D. COR . Hence , if m be any number , mD + mE + mF m.D + E + F . For mD , mE , and mF are multiples of D , E , and F by m , therefore their fum is also a multiple of D + E + F by m . I ...
Side 137
... multiple of the fecond , that the multiple of the third has to the multiple of the fourth . Let Book V. a 3. 5 . Let A : B OF GEOMETRY . 137.
... multiple of the fecond , that the multiple of the third has to the multiple of the fourth . Let Book V. a 3. 5 . Let A : B OF GEOMETRY . 137.
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Almindelige termer og sætninger
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
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Side 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.
Side 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 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...
Side 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.
Side 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...
Side 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...
Side 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.
Side 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...
Side 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.