Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
From inside the book
Results 1-5 of 57
Page v
... taken some from Cress- well , Bland , & c . and added others of his own ; and he trusts it is made so as to meet the approbation of the public in general . There are also algebraic demonstrations annexed to the second and fifth books ...
... taken some from Cress- well , Bland , & c . and added others of his own ; and he trusts it is made so as to meet the approbation of the public in general . There are also algebraic demonstrations annexed to the second and fifth books ...
Page xviii
... taken ; " what gave Marcellus the greatest concern , " says Plu- tarch , " was the unhappy fate of Archimedes , who was at that time in the museum ; so intent was his mind , as well as his eye , upon some geometrical figures , that he ...
... taken ; " what gave Marcellus the greatest concern , " says Plu- tarch , " was the unhappy fate of Archimedes , who was at that time in the museum ; so intent was his mind , as well as his eye , upon some geometrical figures , that he ...
Page xxvi
... taken as true unless demonstrated ; and nothing is demonstrated , but from what went before . In consequence of this rigorous system of demonstration , it is re- ported that king Ptolemy , once asking Euclid whether there was no shorter ...
... taken as true unless demonstrated ; and nothing is demonstrated , but from what went before . In consequence of this rigorous system of demonstration , it is re- ported that king Ptolemy , once asking Euclid whether there was no shorter ...
Page 4
... taken from equals , the remainders are equal . 4. If equals be added to unequals , the wholes are unequal . 5. If equals be taken from unequals , the remainders are unequal . 6. Things which are double of the same , are equal to one ...
... taken from equals , the remainders are equal . 4. If equals be added to unequals , the wholes are unequal . 5. If equals be taken from unequals , the remainders are unequal . 6. Things which are double of the same , are equal to one ...
Page 10
... taken in either of them , AC , bc , the proposition is manifest ; for so the whole ac would be equal to its part AD , or the whole BC equal to its part BD , which is impossible . Dr. Simson , in his note to this proposition , says , he ...
... taken in either of them , AC , bc , the proposition is manifest ; for so the whole ac would be equal to its part AD , or the whole BC equal to its part BD , which is impossible . Dr. Simson , in his note to this proposition , says , he ...
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.