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 6
... 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 , cutting off with the other leg the part required ...
... 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 , cutting off with the other leg the part required ...
Σελίδα 12
... reason is manifest , for the equality of the vertical angles being demonstrated , it follows , that all are equal to all by the fourth . Whence it was only necessary to demonstrate this , and assume the rest as consequents . PROPOSITION ...
... reason is manifest , for the equality of the vertical angles being demonstrated , it follows , that all are equal to all by the fourth . Whence it was only necessary to demonstrate this , and assume the rest as consequents . PROPOSITION ...
Σελίδα 20
... reason , the exterior angle CEB of the triangle ABC is greater than BAC . But the angle BDC was shown to be greater than the angle CEB ; much more then will the angle BDC be greater than the angle BAC . Wherefore if from the ends , & c ...
... reason , the exterior angle CEB of the triangle ABC is greater than BAC . But the angle BDC was shown to be greater than the angle CEB ; much more then will the angle BDC be greater than the angle BAC . Wherefore if from the ends , & c ...
Σελίδα 32
... reason EF is equal to BC . And therefore AD will be equal to EFb and DE common . Therefore the whole AE is equal to the whole DF . But AB is equal to DC . Therefore the two EA , AB , are equal to the two FD , DC , each to each , and the ...
... reason EF is equal to BC . And therefore AD will be equal to EFb and DE common . Therefore the whole AE is equal to the whole DF . But AB is equal to DC . Therefore the two EA , AB , are equal to the two FD , DC , each to each , and the ...
Σελίδα 33
... reason the parallelo- gram EFGH is equal to the parallelogram EBCH , for 35. 1 . it has the same base EH , and is constituted between the same parallels EH , BG . Therefore the parallelogram ABCD will be equal to the parallelogram EFGH ...
... reason the parallelo- gram EFGH is equal to the parallelogram EBCH , for 35. 1 . it has the same base EH , and is constituted between the same parallels EH , BG . Therefore the parallelogram ABCD will be equal to the parallelogram EFGH ...
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.