Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
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Page 2
... figure is that which is contained under one or more terms . 15. A circle is a plane figure contained by one line ... Rectilineal figures are those which are contained by right lines . 20. Triangles are such as are contained by three ...
... figure is that which is contained under one or more terms . 15. A circle is a plane figure contained by one line ... Rectilineal figures are those which are contained by right lines . 20. Triangles are such as are contained by three ...
Page 21
... rectilineal figure of any number of sides , having given the length of each side of all the triangles into which the figure is divided . PROPOSITION XXIII . PROBLEM . * To a given right line , and to a given point in it , to make a ...
... rectilineal figure of any number of sides , having given the length of each side of all the triangles into which the figure is divided . PROPOSITION XXIII . PROBLEM . * To a given right line , and to a given point in it , to make a ...
Page 39
... rectilineal figure , and having an angle equal to a given rectilineal angle . F GL Let ABCD be the given rectilineal figure , and E the given rectilineal angle : it is required to describe a pa- rallelogram equal to the given rec ...
... rectilineal figure , and having an angle equal to a given rectilineal angle . F GL Let ABCD be the given rectilineal figure , and E the given rectilineal angle : it is required to describe a pa- rallelogram equal to the given rec ...
Page 40
... triangle DBC equal to the parallelogram GM . The whole pa- rallelogram KLFM is equal to the whole rectilineal figure ABCD . Therefore the parallelogram KFLM is equal to the given rectilineal figure ABCD , and having the angle FKM equal ...
... triangle DBC equal to the parallelogram GM . The whole pa- rallelogram KLFM is equal to the whole rectilineal figure ABCD . Therefore the parallelogram KFLM is equal to the given rectilineal figure ABCD , and having the angle FKM equal ...
Page 97
... rectilineal figure , when every angle of the inscribed figure touches every side of the figure in which it is in- scribed . * 2. In like manner a figure is said to be circumscribed about a figure , when all the sides of the ...
... rectilineal figure , when every angle of the inscribed figure touches every side of the figure in which it is in- scribed . * 2. In like manner a figure is said to be circumscribed about a figure , when all the sides of the ...
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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.