The Elements of Euclid: With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means of Establishing a Juster Taste Upon Mathematical Subjects Than that which at Present PrevailsPrinted at the Clarendon Press, 1781 - 309 σελίδες |
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Σελίδα 12
... hath been seen alive , ten thousand " times smaller than a mite , may be proved , and yet how much fmaller it may have been is not determined . " 66 " 66 66 A . it It has been said of the mufick of the spheres that it is so loud we ...
... hath been seen alive , ten thousand " times smaller than a mite , may be proved , and yet how much fmaller it may have been is not determined . " 66 " 66 66 A . it It has been said of the mufick of the spheres that it is so loud we ...
Σελίδα 13
... hath length and breadth . But farther this surface has a shape or is limi- ted ; that which limits it cannot have length and breadth ; for then it would not be the limit of the furface but a part of it . Therefore the proper definition ...
... hath length and breadth . But farther this surface has a shape or is limi- ted ; that which limits it cannot have length and breadth ; for then it would not be the limit of the furface but a part of it . Therefore the proper definition ...
Σελίδα 22
... hath already laid down as easy and self evident . His first propofition then is upon a right line given to make an equilateral triangle . He hath defined in the fourth definition what he " means by a right line , namely that which lieth ...
... hath already laid down as easy and self evident . His first propofition then is upon a right line given to make an equilateral triangle . He hath defined in the fourth definition what he " means by a right line , namely that which lieth ...
Σελίδα 14
... hath been drawn at right angles to the given ftraight line the straight line AB , from any point given in it the point C. A F D C E B For fince the straight line CD is equal to the ftraight line CE ( by conft . ) and the straight line ...
... hath been drawn at right angles to the given ftraight line the straight line AB , from any point given in it the point C. A F D C E B For fince the straight line CD is equal to the ftraight line CE ( by conft . ) and the straight line ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe
Δημοφιλή αποσπάσματα
Σελίδα 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 47 - 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. Let...
Σελίδα 68 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Σελίδα 45 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Σελίδα 15 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Σελίδα 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 88 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 42 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Σελίδα 109 - Draw two diameters AC, BD of the circle ABCD, at right angles to one another; and through the points A, B. C, D, draw (17.
Σελίδα 8 - GB is equal to E, and CK to F ; therefore AB is the same multiple of E, that KH is of F: But AB...