Euclid's Elements of geometry, transl. To which are added, algebraic demonstrations to the second and fifth books; also deductions in the first six, eleventh and twelfth books, with notes, by G. Phillips. Part 1, containing book i-vi1826 |
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Página xii
... means of an in- strument consisting of two rules , one of them moved in the grooves of two arms at right angles with the other , so as always to continue parallel with it . But though Plato was unfortunate in his xii INTRODUCTION .
... means of an in- strument consisting of two rules , one of them moved in the grooves of two arms at right angles with the other , so as always to continue parallel with it . But though Plato was unfortunate in his xii INTRODUCTION .
Página xiii
... his labours , it appears that if we possessed the means of de- scribing conic sections by one continued motion , in as simple a way as we trace a circle with the compasses , the solutions of Menechmus would have all the INTRODUCTION . xiii.
... his labours , it appears that if we possessed the means of de- scribing conic sections by one continued motion , in as simple a way as we trace a circle with the compasses , the solutions of Menechmus would have all the INTRODUCTION . xiii.
Página xiv
... means of the rule and compasses only , yet it was reduced to a very neat and simple proposition . This consists in drawing a right line from a given point to the semi - periphery of a circle , which line shall cut this periphery , and ...
... means of the rule and compasses only , yet it was reduced to a very neat and simple proposition . This consists in drawing a right line from a given point to the semi - periphery of a circle , which line shall cut this periphery , and ...
Página xxv
... means of its three sides , without knowing the perpendicular . Having thus far exhibited to the reader those votaries of science who flourished in the first period of her history , with their discoveries and improvements , let us turn ...
... means of its three sides , without knowing the perpendicular . Having thus far exhibited to the reader those votaries of science who flourished in the first period of her history , with their discoveries and improvements , let us turn ...
Página 6
... means approved of the method , as those who thus reason , he says , beg in the very beginning . + Some persons perform this proposition by taking the less line in the compasses , and with one leg in either extremity of the greater ...
... means approved of the method , as those who thus reason , he says , beg in the very beginning . + Some persons perform this proposition by taking the less line in the compasses , and with one leg in either extremity of the greater ...
Términos y frases comunes
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circumference 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 given circle given point given right line gnomon greater ratio hence inscribed isosceles triangle join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deductions Q. E. D. PROPOSITION rectangle contained remaining angle right line AB right line AC right line drawn segment side AC similar and similarly square of AC subtending THEOREM three right lines tiple touches the circle triangle ABC triangle DEF whence whole
Pasajes populares
Página xxx - 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.
Página 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 146 - 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.
Página 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.
Página 2 - Things which are double of the same are equal to one another. 7. Things which are halves of the same are equal to one another.
Página 28 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Página 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.
Página 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.
Página 95 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw (1 7. 3.) the straight line G AH touching the circle in the point A, and. at the point A, in the straight line AH, make (23.