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
... angles . There can be little doubt that he made many other discoveries , which have not been directly handed down to ... right angled triangle is equal to the sum of the squares of the other two sides ( see note to the 47th proposition ...
... angles . There can be little doubt that he made many other discoveries , which have not been directly handed down to ... right angled triangle is equal to the sum of the squares of the other two sides ( see note to the 47th proposition ...
Σελίδα x
... angles of any triangle are together equal to two right angles ; as likewise to have shown that only three polygons , or regular plane figures , can fill up the space about a point ; viz . the equilateral triangle , the square , and the ...
... angles of any triangle are together equal to two right angles ; as likewise to have shown that only three polygons , or regular plane figures , can fill up the space about a point ; viz . the equilateral triangle , the square , and the ...
Σελίδα xii
... right angles with the other , so as always to continue parallel with it . But though Plato was unfortunate in his xii INTRODUCTION .
... right angles with the other , so as always to continue parallel with it . But though Plato was unfortunate in his xii INTRODUCTION .
Σελίδα xxix
... right line is that which lies evenly between its extreme points . 5. A superficies is that which has only length and ... angles equal to one another , each of the equal angles is a right angle , and the right line standing on the other ...
... right line is that which lies evenly between its extreme points . 5. A superficies is that which has only length and ... angles equal to one another , each of the equal angles is a right angle , and the right line standing on the other ...
Σελίδα 1
... angles right angles . 30. An oblong is that which has its angles right angles , but all its sides not equal . 31. A rhombus has its sides equal , but its angles not right angles . 32. A rhomboid has its opposite sides and angles equal ...
... angles right angles . 30. An oblong is that which has its angles right angles , but all its sides not equal . 31. A rhombus has its sides equal , but its angles not right angles . 32. A rhomboid has its opposite sides and angles equal ...
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.