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 7
... angles , other two equal angles ; which may be done by the affiftance of a different corner of the fame piece of wood ; and this will illuftrate the fecond and third ... equal $ сед equal to the angle ACF : and I DISSERTATION I. 7.
... angles , other two equal angles ; which may be done by the affiftance of a different corner of the fame piece of wood ; and this will illuftrate the fecond and third ... equal $ сед equal to the angle ACF : and I DISSERTATION I. 7.
Σελίδα 35
... equal to the two fides DE and DF ; each to each , viz . the fide AB equal to DE ; and the fide AC equal to DF ; and ... angles top , why that epithet remaining ? Why , because only one angle in each triangle being equal by the ...
... equal to the two fides DE and DF ; each to each , viz . the fide AB equal to DE ; and the fide AC equal to DF ; and ... angles top , why that epithet remaining ? Why , because only one angle in each triangle being equal by the ...
Σελίδα 36
... equal by the fuppofition extended under them ; that is the angles under which AB and DE are extended are to be equal , as alfo thofe under which AC and DF are extended ; viz . the angle ACB or BCA equal to the angle DFE or EFD ; and the ...
... equal by the fuppofition extended under them ; that is the angles under which AB and DE are extended are to be equal , as alfo thofe under which AC and DF are extended ; viz . the angle ACB or BCA equal to the angle DFE or EFD ; and the ...
Σελίδα 38
... angles , contained by the equal fides , equal ; it is required to make the third fide , equal to the third fide ; and the two re- maining angles equal to the two remaining angles , each to each ; namely those under which the equal fides ...
... angles , contained by the equal fides , equal ; it is required to make the third fide , equal to the third fide ; and the two re- maining angles equal to the two remaining angles , each to each ; namely those under which the equal fides ...
Σελίδα 39
... equal to DE , and the angle BAC equal to the angle EDF ; but that we are quite in the dark as to AC and DF . When ... angles or inclinations of the lines . * But farther , let us fuppofe , that not only AB is equal to DE and AC to DF and ...
... equal to DE , and the angle BAC equal to the angle EDF ; but that we are quite in the dark as to AC and DF . When ... angles or inclinations of the lines . * But farther , let us fuppofe , that not only AB is equal to DE and AC to DF and ...
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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...