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 |
Inni boken
Resultat 1-5 av 31
Side 37
... rectangle , whose base is the diagonal of the trapezium , and perpendicular the aggregate of the perpendiculars drawn from the vertical angles unto the diagonal . 2. To describe a parallelogram , the area and perimeter of which shall be ...
... rectangle , whose base is the diagonal of the trapezium , and perpendicular the aggregate of the perpendiculars drawn from the vertical angles unto the diagonal . 2. To describe a parallelogram , the area and perimeter of which shall be ...
Side 40
... site sides and angles of parallelograms are equal to one * In like manner a rectangle may be described which is contained under two right lines . another . Therefore each of the opposite angles ABE , 40 [ Book I. EUCLID'S ELEMENTS .
... site sides and angles of parallelograms are equal to one * In like manner a rectangle may be described which is contained under two right lines . another . Therefore each of the opposite angles ABE , 40 [ Book I. EUCLID'S ELEMENTS .
Side 41
... rectangle . But it was shown to be equilateral , there- fore it is a square , and has been described on the given right line AB . Q. E. F. COROLLARY . Hence every parallelogram having one right angle is a rectangle . PROPOSITION XLVII ...
... rectangle . But it was shown to be equilateral , there- fore it is a square , and has been described on the given right line AB . Q. E. F. COROLLARY . Hence every parallelogram having one right angle is a rectangle . PROPOSITION XLVII ...
Side 45
... rectangle comprehended under the whole and divided line , is equal to the rectangles con- tained under the whole line , and the several segments of the divided line . Let A and BC be two right lines , and let BC be any how divided in ...
... rectangle comprehended under the whole and divided line , is equal to the rectangles con- tained under the whole line , and the several segments of the divided line . Let A and BC be two right lines , and let BC be any how divided in ...
Side 46
... rectangle DL is contained under A and DE ; because DK , that is BG , is equal to a ; so likewise the rectangle EH is that contained under a and Ec . Therefore the rectangle under A and BC is equal to the rectangles under A and BD , A ...
... rectangle DL is contained under A and DE ; because DK , that is BG , is equal to a ; so likewise the rectangle EH is that contained under a and Ec . Therefore the rectangle under A and BC is equal to the rectangles under A and BD , A ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 28 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Side 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.
Side 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.
Side 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.