Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 25.
Σελίδα viii
... divided the kingdom among all his subjects , and that he had given each an equal quantity of land , on condition of paying annually a proportionate tribute . If the portion allotted to any one were diminished by the river , he went to ...
... divided the kingdom among all his subjects , and that he had given each an equal quantity of land , on condition of paying annually a proportionate tribute . If the portion allotted to any one were diminished by the river , he went to ...
Σελίδα 6
... divided into a variety of cases according to the different positions of the point a , although the construction and demon- stration will , in every respect , be the same . Proclus remarks that some performed it by taking the line AL ...
... divided into a variety of cases according to the different positions of the point a , although the construction and demon- stration will , in every respect , be the same . Proclus remarks that some performed it by taking the line AL ...
Σελίδα 21
... divided . PROPOSITION XXIII . PROBLEM . * To a given right line , and to a given point in it , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given right line , and a the given point in it ; also DCE the ...
... divided . PROPOSITION XXIII . PROBLEM . * To a given right line , and to a given point in it , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given right line , and a the given point in it ; also DCE the ...
Σελίδα 45
... divided into any number of parts , the 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 ...
... divided into any number of parts , the 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 ...
Σελίδα 46
... divided into the parts e , f , g ; then shall * Ax . 8. 1. ab = ae + af + ag ; for b * = e + ƒ + g , multiply each by a , and we shall have ab = ae + af + ag . Q. E. D.t PROPOSITION II . THEOREM . If a right line be divided into any two ...
... divided into the parts e , f , g ; then shall * Ax . 8. 1. ab = ae + af + ag ; for b * = e + ƒ + g , multiply each by a , and we shall have ab = ae + af + ag . Q. E. D.t PROPOSITION II . THEOREM . If a right line be divided into any two ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry; Containing the First Six Books of Euclid ... Euclid,John Playfair Πλήρης προβολή - 1814 |
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 circum circumference BC 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 Geometry given circle given point given right line gnomon greater ratio hence inscribed join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deduction Q. E. D. PROPOSITION rectangle contained remaining angle right angles right line AB right line AC sector HEF segment side BC similar and similarly square of AC subtending THEOREM tiple touches the circle triangle ABC triangle DEF whence whole
Δημοφιλή αποσπάσματα
Σελίδα xxvi - 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 148 - 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 8 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
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 99 - To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. . Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, • 17.3. C, D, draw...
Σελίδα 7 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Σελίδα 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.