Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
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Page ix
... applied the circumference of the circle in measuring angles . There can be little doubt that he made many other discoveries , which have not been directly handed down to us , but which might have been inserted in elementary books , and ...
... applied the circumference of the circle in measuring angles . There can be little doubt that he made many other discoveries , which have not been directly handed down to us , but which might have been inserted in elementary books , and ...
Page xiv
... applied to the term . But at present no instruments have been made that will describe the conic sections in this manner . I cannot , however , pass over the problem of the trisection of an angle , which is of the same kind with that of ...
... applied to the term . But at present no instruments have been made that will describe the conic sections in this manner . I cannot , however , pass over the problem of the trisection of an angle , which is of the same kind with that of ...
Page xv
... applied themselves to the study of the mathematics . The former wrote a History of the Mathematics in eleven books , from their origin to his own time , four of which treated on Geometry , six on Astronomy , and one on Arithmetic . The ...
... applied themselves to the study of the mathematics . The former wrote a History of the Mathematics in eleven books , from their origin to his own time , four of which treated on Geometry , six on Astronomy , and one on Arithmetic . The ...
Page xvii
... applied himself closely to the measuring of conic sections , as well as other figures . He determined the relations of spheres , spheroids , and conoids , to cylinders and cones , and the relations of parabolas to rectilineal planes ...
... applied himself closely to the measuring of conic sections , as well as other figures . He determined the relations of spheres , spheroids , and conoids , to cylinders and cones , and the relations of parabolas to rectilineal planes ...
Page 7
... applied to the triangle DEF , and the point a be put upon the point D , and the right line AB upon the right line DE , then shall the point B coincide with the point E , because AB is equal to DE . But AB coinciding with DE ; the right ...
... applied to the triangle DEF , and the point a be put upon the point D , and the right line AB upon the right line DE , then shall the point B coincide with the point E , because AB is equal to DE . But AB coinciding with DE ; the right ...
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Common terms and phrases
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circum circumference BC diameter double draw equal angles equal circles equal right lines equal to F equi equiangular equimultiples Euclid EUCLID'S ELEMENTS exceed exterior angle fore four magnitudes fourth Geometry given circle given point given right line gnomon greater ratio hence inscribed join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deduction Q. E. D. PROPOSITION rectangle contained remaining angle right angles right line AB right line AC sector HEF segment side BC similar and similarly square of AC subtending THEOREM tiple touches the circle triangle ABC triangle DEF whence whole
Popular passages
Page xxvi - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Page 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 148 - 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 27 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Page 8 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Page 73 - DH; (I. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Page 99 - To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. . Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, • 17.3. C, D, draw...
Page 7 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Page 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.