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 23
... triangle ABC ; which was defired . This is " the first part of the pro- “ blem , and indeed the + difficultest to find out ; " namely how to do the 66 66 66 thing required ; and in this part lie the greatest " difficulties of mathema ...
... triangle ABC ; which was defired . This is " the first part of the pro- “ blem , and indeed the + difficultest to find out ; " namely how to do the 66 66 66 thing required ; and in this part lie the greatest " difficulties of mathema ...
Página 26
... ABC was an equilateral triangle ; and there could be but " two fuch made upon the line AB in the fame plain ; there being " but two points where in those circles cut each other ; thofe cir- " cles determining all the lines equal to AB ...
... ABC was an equilateral triangle ; and there could be but " two fuch made upon the line AB in the fame plain ; there being " but two points where in those circles cut each other ; thofe cir- " cles determining all the lines equal to AB ...
Página 29
... triangle ABC to be an affignable or determinate mag- nitude implies that the points A , B , C have no magnitude for if they had parts various triangles differing both in fides and angles . might be described , and it would be impoffible ...
... triangle ABC to be an affignable or determinate mag- nitude implies that the points A , B , C have no magnitude for if they had parts various triangles differing both in fides and angles . might be described , and it would be impoffible ...
Página 35
... ABC and DEF be two A D triangles ; having the two fides AB and AC equal to the two fides DE and DF ; each to each ... triangle ABC equal to the whole triangle DEF : and the remaining angles top , why that epithet remaining ? Why ...
... ABC and DEF be two A D triangles ; having the two fides AB and AC equal to the two fides DE and DF ; each to each ... triangle ABC equal to the whole triangle DEF : and the remaining angles top , why that epithet remaining ? Why ...
Página 39
... triangles as in the propofition , we fhall find the angle ABC equal to DEF ; and not only that , but , by putting A ... triangle DEF are equal : But this conclufion does not depend entirely upon DE's being equal to DF ; but it is ...
... triangles as in the propofition , we fhall find the angle ABC equal to DEF ; and not only that , but , by putting A ... triangle DEF are equal : But this conclufion does not depend entirely upon DE's being equal to DF ; but it is ...
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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...