Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
From inside the book
Results 1-5 of 30
Page xiii
Euclid. with it . But though Plato was unfortunate in his attempts to double the cube , yet we find him more successful in another speculation of a kind entirely new . Before his time the circle was the only curve admitted into geometry ...
Euclid. with it . But though Plato was unfortunate in his attempts to double the cube , yet we find him more successful in another speculation of a kind entirely new . Before his time the circle was the only curve admitted into geometry ...
Page 4
... double of the same , are equal to one another . 7. Things which are halves of the same , are equal to one another . 8. Things which mutually agree with one another , are equal to one another . 9. The whole is greater than its part ...
... double of the same , are equal to one another . 7. Things which are halves of the same , are equal to one another . 8. Things which mutually agree with one another , are equal to one another . 9. The whole is greater than its part ...
Page 30
... double the angle contained by the line bisecting the vertical angle and another drawn from the vertex perpendicular to the base . 3. Given the difference of the angles at the base of a triangle , the perpendicular drawn from the vertex ...
... double the angle contained by the line bisecting the vertical angle and another drawn from the vertex perpendicular to the base . 3. Given the difference of the angles at the base of a triangle , the perpendicular drawn from the vertex ...
Page 36
... double of the triangle . A D B C E For let ABCD be a parallelogram , and EBC a triangle ; let them have the same base BC , and between the same parallels BC , AE . The parallelo- gram ABCD , is double of the triangle EBC . For join AC ...
... double of the triangle . A D B C E For let ABCD be a parallelogram , and EBC a triangle ; let them have the same base BC , and between the same parallels BC , AE . The parallelo- gram ABCD , is double of the triangle EBC . For join AC ...
Page 37
... double of the triangle AEC . But the parallelogram FECG is also double of the triangle AEC , because it has the same base , and is between the 41. 1 . same parallels . Therefore the parallelogram FECG is equal to the triangle ABC , and ...
... double of the triangle AEC . But the parallelogram FECG is also double of the triangle AEC , because it has the same base , and is between the 41. 1 . same parallels . Therefore the parallelogram FECG is equal to the triangle ABC , and ...
Other editions - View all
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.