The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα
... it will be followed by other works carrying the subject forward . A number of Exercises on each book have been given , the solu- tions of which will be published separately . CONTENTS . BOOK I. Definitions , & c . Propositions.
... it will be followed by other works carrying the subject forward . A number of Exercises on each book have been given , the solu- tions of which will be published separately . CONTENTS . BOOK I. Definitions , & c . Propositions.
Σελίδα
... Definitions Propositions Exercises IV . Definitions Propositions Exercises V. Definitions Propositions Exercises VI . Definitions Propositions Exercises PAGE 1 4 33 35 35 46 47 48 73 75 76 87 89 91 115 • 116 116 146 THE ELEMENTS OF OF ...
... Definitions Propositions Exercises IV . Definitions Propositions Exercises V. Definitions Propositions Exercises VI . Definitions Propositions Exercises PAGE 1 4 33 35 35 46 47 48 73 75 76 87 89 91 115 • 116 116 146 THE ELEMENTS OF OF ...
Σελίδα 1
Euclides. THE ELEMENTS OF OF EUCLID . BOOK I. DEFINITIONS . I. A POINT is that which hath no parts , or which hath no magnitude . II . A line is length without breadth . III . The extremities of a line are points . IV . A ... Definitions, &c.
Euclides. THE ELEMENTS OF OF EUCLID . BOOK I. DEFINITIONS . I. A POINT is that which hath no parts , or which hath no magnitude . II . A line is length without breadth . III . The extremities of a line are points . IV . A ... Definitions, &c.
Σελίδα 3
... these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS .
... these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS .
Σελίδα 34
... given parallelo- gram , the diameters of all the figures shall cut one another in the same point . 26. In a parallelogram the diameters bisect each other . BOOK II . DEFINITIONS . I. EVERY right - angled 34 THE ELEMENTS OF EUCLID .
... given parallelo- gram , the diameters of all the figures shall cut one another in the same point . 26. In a parallelogram the diameters bisect each other . BOOK II . DEFINITIONS . I. EVERY right - angled 34 THE ELEMENTS OF EUCLID .
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Συχνά εμφανιζόμενοι όροι και φράσεις
a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular Q. E. D. PROPOSITION rectangle a b rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 40 - 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.
Σελίδα 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 27 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Σελίδα 13 - If, from the ends of the 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. Let...
Σελίδα 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 124 - 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.