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 sider |
Inni boken
Resultat 1-5 av 20
Side 83
... circle , touches the circle : and that a straight line touches a circle in one point only : because ( by 2. 3. ) the ftraight line meet- ing it in two points has been fhewn to fall within it . PROP . XVII . From a given point to draw a ...
... circle , touches the circle : and that a straight line touches a circle in one point only : because ( by 2. 3. ) the ftraight line meet- ing it in two points has been fhewn to fall within it . PROP . XVII . From a given point to draw a ...
Side 84
... touch a circle , and any straight line be drawn from the center to the point of contact ; the line drawn will be perpendicular to the touching line . Let any straight line DE touch the circle ABC , in the point C ; and let F the center of ...
... touch a circle , and any straight line be drawn from the center to the point of contact ; the line drawn will be perpendicular to the touching line . Let any straight line DE touch the circle ABC , in the point C ; and let F the center of ...
Side 85
... circle ABC : certainly in the fame manner we shall demonstrate , that neither is it any other , but some point in AC . Wherefore if any straight line touch ... touching line the center of the circle will be in the line fo drawn . Which was to ...
... circle ABC : certainly in the fame manner we shall demonstrate , that neither is it any other , but some point in AC . Wherefore if any straight line touch ... touching line the center of the circle will be in the line fo drawn . Which was to ...
Side 94
... touch a circle ; and if from the contact any . straight line be drawn to the circle , cutting the circle ; the angles which it makes with the touching line will be equal to the angles in the alternate fegments of the circle . For let ...
... touch a circle ; and if from the contact any . straight line be drawn to the circle , cutting the circle ; the angles which it makes with the touching line will be equal to the angles in the alternate fegments of the circle . For let ...
Side 95
... touches the circle ABCD in the point B ; and from the contact at B the straight line AB has been drawn at right angles to the touching line ; the center of the circle ABCD is ( by 19. 3. ) in the straight line AB : therefore the angle ...
... touches the circle ABCD in the point B ; and from the contact at B the straight line AB has been drawn at right angles to the touching line ; the center of the circle ABCD is ( by 19. 3. ) in the straight line AB : therefore the angle ...
Andre utgaver - Vis alle
The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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...
Side 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.
Side 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.
Side 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.
Side 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.
Side 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...