The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 6
... Note on the 29th Propo- sition , Book 1st , is altered , and made more explicit , and a more general Demonstration is given , instead of that which was in the Note on the 10th Definition of Book 11th ; besides , the Translation is much ...
... Note on the 29th Propo- sition , Book 1st , is altered , and made more explicit , and a more general Demonstration is given , instead of that which was in the Note on the 10th Definition of Book 11th ; besides , the Translation is much ...
Σελίδα 17
... CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but it has been demon- strated to be greater than it ; which is impossible . See Note . C But if one of the vertices , as D , BOOK I. 17 THE ELEMENTS OF EUCLID .
... CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but it has been demon- strated to be greater than it ; which is impossible . See Note . C But if one of the vertices , as D , BOOK I. 17 THE ELEMENTS OF EUCLID .
Σελίδα 20
... straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC is a straight * See Note . line , the angle CBE is equal ( 10 . 20 BOOK I. THE ELEMENTS OF EUCLID .
... straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC is a straight * See Note . line , the angle CBE is equal ( 10 . 20 BOOK I. THE ELEMENTS OF EUCLID .
Σελίδα 27
... KG ; the tri- angle KFG has its sides D equal to the three straight lines A , B , C. K E F G H L Because the point F is the centre of the circle BKL , FD is • See Note . equal ( 15. Def . ) to FK ; but BOOK I. 27 THE ELEMENTS OF EUCLID .
... KG ; the tri- angle KFG has its sides D equal to the three straight lines A , B , C. K E F G H L Because the point F is the centre of the circle BKL , FD is • See Note . equal ( 15. Def . ) to FK ; but BOOK I. 27 THE ELEMENTS OF EUCLID .
Σελίδα 62
... , CD : to these equals add the square of BC , and the squares of AB , BC are equal to the square of AC , and twice the square of B * See Note . C D BC , and twice the rectangle BC , CD : 62 BOOK II . THE ELEMENTS OF EUCLID .
... , CD : to these equals add the square of BC , and the squares of AB , BC are equal to the square of AC , and twice the square of B * See Note . C D BC , and twice the rectangle BC , CD : 62 BOOK II . THE ELEMENTS OF EUCLID .
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 81 - The angles in the same segment of a circle are equal to one another.
Σελίδα 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Σελίδα 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Σελίδα 24 - Any two sides of a triangle are together greater than the third side.