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 viii
... given figure as a base , a solid may be constituted , or conceived to exist , equal in solid contents to any given solid , ( be- cause a solid , whatever be its base , as its height may be indefinitely varied , is capable of all degrees ...
... given figure as a base , a solid may be constituted , or conceived to exist , equal in solid contents to any given solid , ( be- cause a solid , whatever be its base , as its height may be indefinitely varied , is capable of all degrees ...
Page ix
... given base a solid of a given magni- tude may be constituted , is one of those , by the introduc- tion of which , the Geometry of solids is much shortened , while all the real accuracy of the demonstrations is pre- served ; and ...
... given base a solid of a given magni- tude may be constituted , is one of those , by the introduc- tion of which , the Geometry of solids is much shortened , while all the real accuracy of the demonstrations is pre- served ; and ...
Page 18
... given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the ... given straight line AB . Which was required to be done . PROP . II . PROB . From a given point to draw a straight line ...
... given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the ... given straight line AB . Which was required to be done . PROP . II . PROB . From a given point to draw a straight line ...
Page 19
... given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
... given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
Page 23
... given rectilineal angle , that is , to divide it into two equal angles . • Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AF equal to AD ; join DE , and upon ...
... given rectilineal angle , that is , to divide it into two equal angles . • Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AF equal to AD ; join DE , and upon ...
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Common terms and phrases
ABC is equal ABCD adjacent angles 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 meet multiple opposite angle parallel 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 125 - 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 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Page 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 19 - BG; and 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.
Page 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Page 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Page 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Page 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Page 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.