The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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Σελίδα 154
... proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . x . When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
... proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . x . When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
Σελίδα 156
... proportion ; when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and the second to the third of the first rank , as the second to the third of the other ; and so on in order ; and ...
... proportion ; when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and the second to the third of the first rank , as the second to the third of the other ; and so on in order ; and ...
Σελίδα 225
... proportion . 10. If ABC be an inscribed triangle , and BD be drawn parallel to the tangent at A to meet AC , or AC produced , shew that AB is a mean proportional between AC , AD . 11. AB is divided in C , D , so that AB : AC :: AC : AD ...
... proportion . 10. If ABC be an inscribed triangle , and BD be drawn parallel to the tangent at A to meet AC , or AC produced , shew that AB is a mean proportional between AC , AD . 11. AB is divided in C , D , so that AB : AC :: AC : AD ...
Σελίδα 227
... proportion . The Proportion in ( iii ) is often thus expressed , AB : AD :: CB : CD , or AD : AB :: CD : CB or AD.BC = AB.CD . 1 A B C D 34. If the two angles , which one straight line BOOK VI . 227.
... proportion . The Proportion in ( iii ) is often thus expressed , AB : AD :: CB : CD , or AD : AB :: CD : CB or AD.BC = AB.CD . 1 A B C D 34. If the two angles , which one straight line BOOK VI . 227.
Σελίδα 234
... Bg , Bh , & c . are in harmonic proportion . 100. If pairs of common tangents be drawn to each two of three given circles , the intersections of each pair will lie in one line . BOOK XI . DEFINITIONS . 1. A SOLID is that 234 PROBLEMS .
... Bg , Bh , & c . are in harmonic proportion . 100. If pairs of common tangents be drawn to each two of three given circles , the intersections of each pair will lie in one line . BOOK XI . DEFINITIONS . 1. A SOLID is that 234 PROBLEMS .
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 42 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 33 - F, which is the common vertex of the triangles: that is », together with four right angles. Therefore all the angles of the figure, together with four right angles are equal to twice as many right angles as the figure has sides.
Σελίδα 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Σελίδα 194 - 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 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Σελίδα 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.