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 iv
... thing new in Elementary Geome- try would have been soon attempted . But his design was different : it was his object to restore the writings of Euclid to their original perfection , and to give them to Modern Europe as nearly as ...
... thing new in Elementary Geome- try would have been soon attempted . But his design was different : it was his object to restore the writings of Euclid to their original perfection , and to give them to Modern Europe as nearly as ...
Page v
... thing from the rigour of geometrical demonstration . By this means , the steps of the reasoning which were before far separated , are brought near to one another , and the force of the whole is so clearly and directly perceived , that I ...
... thing from the rigour of geometrical demonstration . By this means , the steps of the reasoning which were before far separated , are brought near to one another , and the force of the whole is so clearly and directly perceived , that I ...
Page viii
... thing to be supposed , unless the thing itself be actually exhibited . But it is not always necessary to make use of this defence ; for the existence of many things is obviously possible , and very far from implying a contradiction ...
... thing to be supposed , unless the thing itself be actually exhibited . But it is not always necessary to make use of this defence ; for the existence of many things is obviously possible , and very far from implying a contradiction ...
Page ix
... things has thrown in its way . It is a rule , too , which cannot al- ways be followed , and from which even Euclid himself ... thing not essential . That it may be the better understood , and because the demon- strations which require ...
... things has thrown in its way . It is a rule , too , which cannot al- ways be followed , and from which even Euclid himself ... thing not essential . That it may be the better understood , and because the demon- strations which require ...
Page xi
... thing that ad- mits of being proved . Indeed those who make the ob- jection just stated , do not seem to have reflected suffi- ciently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain ...
... thing that ad- mits of being proved . Indeed those who make the ob- jection just stated , do not seem to have reflected suffi- ciently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain ...
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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.