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 8
... say , unless they were acquired by an exami- nation of particulars , he will find his notions fit every thing fo well , that when he comes to apply them to particular instances , he will not be able to tell which is which . The reader ...
... say , unless they were acquired by an exami- nation of particulars , he will find his notions fit every thing fo well , that when he comes to apply them to particular instances , he will not be able to tell which is which . The reader ...
Página 35
... say I understand now what the author means ; he affirms that all triangles which agree with one another in the circumftances above mentioned cannot poffibly fail in giving us the fame confequences . But let us see what confequences he ...
... say I understand now what the author means ; he affirms that all triangles which agree with one another in the circumftances above mentioned cannot poffibly fail in giving us the fame confequences . But let us see what confequences he ...
Página 40
... say from this that any thing is equal , but what is made equal ; no doubt a very curious discovery and tending greatly to the enlarging the boundaries of the science ! The mistake here arifes from not confidering that it is impof- fible ...
... say from this that any thing is equal , but what is made equal ; no doubt a very curious discovery and tending greatly to the enlarging the boundaries of the science ! The mistake here arifes from not confidering that it is impof- fible ...
Página 60
... say that a line intersecting one of two parallels , would meet the other ; and indeed if this could be fhewn upon fcientific prin- ciples , it would be a demonftration of the thing in queftion : but this would be taking the thirtieth ...
... say that a line intersecting one of two parallels , would meet the other ; and indeed if this could be fhewn upon fcientific prin- ciples , it would be a demonftration of the thing in queftion : but this would be taking the thirtieth ...
Página 88
... says belong to them ; but it would be the greatest abfurdity to call this an illustration of Euclid's demon- ftrations ; as the two methods are founded upon principles , in a certain sense directly contrary to each other : these ...
... says belong to them ; but it would be the greatest abfurdity to call this an illustration of Euclid's demon- ftrations ; as the two methods are founded upon principles , in a certain sense directly contrary to each other : these ...
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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...