Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
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Page v
... meet the approbation of the public in general . There are also algebraic demonstrations annexed to the second and fifth books ; for in these the Editor believes that ana- lysis is generally employed as well in the Uni- versities as in ...
... meet the approbation of the public in general . There are also algebraic demonstrations annexed to the second and fifth books ; for in these the Editor believes that ana- lysis is generally employed as well in the Uni- versities as in ...
Page 3
... meet one another . * POSTULATES . 1. Grant , that a right line may be drawn from any one point to any other point . 2. That a finite right line may be produced directly forwards . 3. That a circle may be described with any distance and ...
... meet one another . * POSTULATES . 1. Grant , that a right line may be drawn from any one point to any other point . 2. That a finite right line may be produced directly forwards . 3. That a circle may be described with any distance and ...
Page 25
... meet towards the parts BD . In like manner we may demonstrate they do not meet * The student must understand that the lines are in the same plane , other- wise the alternate angles might be equal ; and the lines might or might not be ...
... meet towards the parts BD . In like manner we may demonstrate they do not meet * The student must understand that the lines are in the same plane , other- wise the alternate angles might be equal ; and the lines might or might not be ...
Page 26
... meet towards neither parts are parallel . Therefore AB is parallel to CD . Wherefore a right line , & c . Q. E. D. Deduction . If ABCD be a parallelogram , and BH be equal to DG , the tri- angle BFH is equal to the triangle DGE ; also ...
... meet towards neither parts are parallel . Therefore AB is parallel to CD . Wherefore a right line , & c . Q. E. D. Deduction . If ABCD be a parallelogram , and BH be equal to DG , the tri- angle BFH is equal to the triangle DGE ; also ...
Page 27
... meet , if produced far enough.bb Ax . 12 . Therefore the right lines AB , CD , produced far enough , will meet . But they do not meet , since they are parallel . Therefore the angle AGH is not unequal to the angle GHD ; wherefore it is ...
... meet , if produced far enough.bb Ax . 12 . Therefore the right lines AB , CD , produced far enough , will meet . But they do not meet , since they are parallel . Therefore the angle AGH is not unequal to the angle GHD ; wherefore it is ...
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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.