Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 σελίδες |
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Σελίδα 116
... equimultiples of the first and third compared with the equimultiples of the second second , than the third is when compared to the fourth , the first is said to have to the second a greater ratio than the third has to the fourth . " " 4 ...
... equimultiples of the first and third compared with the equimultiples of the second second , than the third is when compared to the fourth , the first is said to have to the second a greater ratio than the third has to the fourth . " " 4 ...
Σελίδα 117
... equimultiples , the multiple of the first exceeds the multiple of the second , but the multiple of the third does not exceed the mul- tiple of the fourth , then the first is said to have a greater ratio to the second , than the third ...
... equimultiples , the multiple of the first exceeds the multiple of the second , but the multiple of the third does not exceed the mul- tiple of the fourth , then the first is said to have a greater ratio to the second , than the third ...
Σελίδα 118
... as some other magnitude F is to the antecedent c ; then is this proportion called perturbate . For further elucidation , consult Fenn's Euclid , page 167 . AXIOMS . 1. " Equimultiples of the same , or 118 [ Book V. EUCLID'S ELEMENTS .
... as some other magnitude F is to the antecedent c ; then is this proportion called perturbate . For further elucidation , consult Fenn's Euclid , page 167 . AXIOMS . 1. " Equimultiples of the same , or 118 [ Book V. EUCLID'S ELEMENTS .
Σελίδα 119
Euclid. AXIOMS . 1. " Equimultiples of the same , or of equal magni- tudes , are equal to one another . " 2. " Those magnitudes of which the same , or equal magnitudes , are equimultiples , are equal to one another . " 3. " A multiple of ...
Euclid. AXIOMS . 1. " Equimultiples of the same , or of equal magni- tudes , are equal to one another . " 2. " Those magnitudes of which the same , or equal magnitudes , are equimultiples , are equal to one another . " 3. " A multiple of ...
Σελίδα 120
Euclid. PROPOSITION I. THEOREM . If there be any number of magnitudes equimultiples of as many other magnitudes ... equi- multiples of as many other magnitudes E , F , each of each ; whatsoever multiple AB is of E , the same mul- tiple AB ...
Euclid. PROPOSITION I. THEOREM . If there be any number of magnitudes equimultiples of as many other magnitudes ... equi- multiples of as many other magnitudes E , F , each of each ; whatsoever multiple AB is of E , the same mul- tiple AB ...
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.