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 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
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.