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 Prevails |
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Page 5
... fore at the porch , not only lend the learner my advice but also my affiftance in ftriping himself of those prejudices which would dif- grace his behaviour after he has been admitted into this magni- ficent temple where all the wonders ...
... fore at the porch , not only lend the learner my advice but also my affiftance in ftriping himself of those prejudices which would dif- grace his behaviour after he has been admitted into this magni- ficent temple where all the wonders ...
Page 11
... fore - mentioned ; for fince all quantity is divi- " fible in infinitum , the least quantity , may be divided as often as " the greatest , and therefore whatsoever is divifible must have parts , and therefore none of these can be ...
... fore - mentioned ; for fince all quantity is divi- " fible in infinitum , the least quantity , may be divided as often as " the greatest , and therefore whatsoever is divifible must have parts , and therefore none of these can be ...
Page 13
... fore the proper definition of a furface will be , that which hath length and breadth . But farther this surface has a shape or is limi- ted ; that which limits it cannot have length and breadth ; for then it would not be the limit of ...
... fore the proper definition of a furface will be , that which hath length and breadth . But farther this surface has a shape or is limi- ted ; that which limits it cannot have length and breadth ; for then it would not be the limit of ...
Page 25
... fore our store , we have no other medium to make a line equal to “ a line , than first by the help of a circle , defined definition 15 . " which by the third poftulatum is granted to be defcribable upon any center and at any distance ...
... fore our store , we have no other medium to make a line equal to “ a line , than first by the help of a circle , defined definition 15 . " which by the third poftulatum is granted to be defcribable upon any center and at any distance ...
Page 60
... fore without perplexing his reader with impotent attempts towards a demonstration ; he judged it more proper to cut short this fruit- let's fearch by placing this principle among the common notions ; and as it appears from this ...
... fore without perplexing his reader with impotent attempts towards a demonstration ; he judged it more proper to cut short this fruit- let's fearch by placing this principle among the common notions ; and as it appears from this ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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...
Page 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.
Page 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.
Page 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.
Page 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 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.
Page 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.
Page 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.
Page 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...