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 páginas |
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Página 91
... segments , but the most natural step to it seems to be the proving that the angles in any femicircle are right angles , and that there seemed to be no other circumstance about a segment fixt except the angles which it contained . Thofe ...
... segments , but the most natural step to it seems to be the proving that the angles in any femicircle are right angles , and that there seemed to be no other circumstance about a segment fixt except the angles which it contained . Thofe ...
Página 92
... segments ; and the equal rectangles made by the segments of lines terminated by it . We may fay indeed that they are all ultimately derived from the center ; but it appears to me that the student will find it very useful to confider ...
... segments ; and the equal rectangles made by the segments of lines terminated by it . We may fay indeed that they are all ultimately derived from the center ; but it appears to me that the student will find it very useful to confider ...
Página 2
... SEGMENT of a circle is the figure bounded by any straight line and the circumference of a circle . 20. The figures bounded by straight lines are called RECTILINEAL FIGURES . 21. Of thefe , fuch as fuch as are bounded by three , are ...
... SEGMENT of a circle is the figure bounded by any straight line and the circumference of a circle . 20. The figures bounded by straight lines are called RECTILINEAL FIGURES . 21. Of thefe , fuch as fuch as are bounded by three , are ...
Página 48
... segments of the divided line . Which was to be demonstrated . PROP . II . If a straight line be cut as it may happen , the rectangles con- tained by the whole and each of the fegments are equal to the fquare of the whole line . For let ...
... segments of the divided line . Which was to be demonstrated . PROP . II . If a straight line be cut as it may happen , the rectangles con- tained by the whole and each of the fegments are equal to the fquare of the whole line . For let ...
Página 49
... segments are equal to the fquare of the whole line . PROP . III . If a straight line be cut as it may happen , the rectangle contai- ned by the whole and one of the fegments is equal to the rectangle contained by the two segments ; and ...
... segments are equal to the fquare of the whole line . PROP . III . If a straight line be cut as it may happen , the rectangle contai- ned by the whole and one of the fegments is equal to the rectangle contained by the two segments ; and ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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...
Página 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.
Página 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.
Página 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.
Página 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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.
Página 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.
Página 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.
Página 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...