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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Σελίδα ix
... applied the circumference of the circle in measuring angles . There can be little doubt that he made many other discoveries , which have not been directly handed down to us , but which might have been inserted in elementary books , and ...
... applied the circumference of the circle in measuring angles . There can be little doubt that he made many other discoveries , which have not been directly handed down to us , but which might have been inserted in elementary books , and ...
Σελίδα xiv
... applied to the term . But at present no instruments have been made that will describe the conic sections in this manner . I cannot , however , pass over the problem of the trisection of an angle , which is of the same kind with that of ...
... applied to the term . But at present no instruments have been made that will describe the conic sections in this manner . I cannot , however , pass over the problem of the trisection of an angle , which is of the same kind with that of ...
Σελίδα xv
... applied themselves to the study of the mathematics . The former wrote a History of the Mathematics in eleven books , from their origin to his own time , four of which treated on Geometry , six on Astronomy , and one on Arithmetic . The ...
... applied themselves to the study of the mathematics . The former wrote a History of the Mathematics in eleven books , from their origin to his own time , four of which treated on Geometry , six on Astronomy , and one on Arithmetic . The ...
Σελίδα xvii
... applied himself closely to the measuring of conic sections , as well as other figures . He determined the relations of spheres , spheroids , and conoids , to cylinders and cones , and the relations of parabolas to rectilineal planes ...
... applied himself closely to the measuring of conic sections , as well as other figures . He determined the relations of spheres , spheroids , and conoids , to cylinders and cones , and the relations of parabolas to rectilineal planes ...
Σελίδα 6
... applied to the triangle DEF , and the point A be put upon the point D , and the right line AB upon the right line DE , then shall the point в coincide with the point E , because AB is equal to DE . But AB coinciding with DE ; the right ...
... applied to the triangle DEF , and the point A be put upon the point D , and the right line AB upon the right line DE , then shall the point в coincide with the point E , because AB is equal to DE . But AB coinciding with DE ; the right ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 28 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 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.