The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 6
... Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and not affumed ; and , therefore , though this were a true Propo- fition , it ought to have been ...
... Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and not affumed ; and , therefore , though this were a true Propo- fition , it ought to have been ...
Σελίδα 119
... magnitude is faid to be a part of a greater magni- tude , when the lefs measures the greater , that is , when the lefs is contained a certain number of times exactly in the greater . ' II . A greater magnitude is faid to be a multiple ...
... magnitude is faid to be a part of a greater magni- tude , when the lefs measures the greater , that is , when the lefs is contained a certain number of times exactly in the greater . ' II . A greater magnitude is faid to be a multiple ...
Σελίδα 120
... Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals ... magnitude . For example , If A , B , C , D be four magnitudes of the fame kind , the first A is faid to have to the ...
... Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals ... magnitude . For example , If A , B , C , D be four magnitudes of the fame kind , the first A is faid to have to the ...
Σελίδα 122
... magnitudes are taken two and two . ' XIX . Ex aequali , from equality ; this term is ufed fimply by itself , when the first magnitude is to the fecond of the first rank , as the first to the fecond of the other rank ; and as the fe ...
... magnitudes are taken two and two . ' XIX . Ex aequali , from equality ; this term is ufed fimply by itself , when the first magnitude is to the fecond of the first rank , as the first to the fecond of the other rank ; and as the fe ...
Σελίδα 123
... magnitude is greater than the fame multiple of a lefs . IV . That magnitude of which a multiple is greater than the fame multiple of another , is greater than that other magnitude . PROP . I. THEOR . 1 F any number of magnitudes be ...
... magnitude is greater than the fame multiple of a lefs . IV . That magnitude of which a multiple is greater than the fame multiple of another , is greater than that other magnitude . PROP . I. THEOR . 1 F any number of magnitudes be ...
Άλλες εκδόσεις - Προβολή όλων
The First Six Books: Together with the Eleventh and Twelfth Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore
Δημοφιλή αποσπάσματα
Σελίδα 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 170 - 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 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Σελίδα 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Σελίδα 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 62 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Σελίδα 200 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 38 - 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.