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
... fore the whole triangle ABC will coincide with the whole triangle DEF , and will be equal to it ; also the remain- ing angles will coincide with the remaining angles , and equal to them , b viz . , the angle ABC to the angle DEF , Ax ...
... fore the whole triangle ABC will coincide with the whole triangle DEF , and will be equal to it ; also the remain- ing angles will coincide with the remaining angles , and equal to them , b viz . , the angle ABC to the angle DEF , Ax ...
Σελίδα 6
... fore the base Fc is equal to the base GB , and the tri- angle AFC equal to the triangle AGB ; also the remain- ing angles shall be equal to the remaining angles , each to each , viz . , the angle ACF equal to the angle ABG ; also the ...
... fore the base Fc is equal to the base GB , and the tri- angle AFC equal to the triangle AGB ; also the remain- ing angles shall be equal to the remaining angles , each to each , viz . , the angle ACF equal to the angle ABG ; also the ...
Σελίδα 8
... fore the base Fc is equal to the base GB , and the tri- angle AFC equal to the triangle AGB ; also the remain- ing angles shall be equal to the remaining angles , each to each , viz . , the angle ACF equal to the angle ABG ; also the ...
... fore the base Fc is equal to the base GB , and the tri- angle AFC equal to the triangle AGB ; also the remain- ing angles shall be equal to the remaining angles , each to each , viz . , the angle ACF equal to the angle ABG ; also the ...
Σελίδα 16
... fore BD will be in a right line with BC . If therefore to a certain right line , & c . Q. E. D. b PROPOSITION XV . THEOREM . * If two right lines cut one another , they will make the vertical angles equal to one another . For let the ...
... fore BD will be in a right line with BC . If therefore to a certain right line , & c . Q. E. D. b PROPOSITION XV . THEOREM . * If two right lines cut one another , they will make the vertical angles equal to one another . For let the ...
Σελίδα 18
... fore the angles ACD , ACB , are greater than the angles ABC , ACB . But ACD , B ACB , are equal to two right angles , D whence ABC , BCA , are less than two right angles . In like manner , we may demonstrate also that the angles BAC ...
... fore the angles ACD , ACB , are greater than the angles ABC , ACB . But ACD , B ACB , are equal to two right angles , D whence ABC , BCA , are less than two right angles . In like manner , we may demonstrate also that the angles BAC ...
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.