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 Seiten |
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Seite 18
... magnitudes which go to the making it up ; viz . three fides and three angles ; each of which ought to be particularly attended to . It will be useful alo to obferve ; that the triangles ABG , ACF though they have feveral parts in common ...
... magnitudes which go to the making it up ; viz . three fides and three angles ; each of which ought to be particularly attended to . It will be useful alo to obferve ; that the triangles ABG , ACF though they have feveral parts in common ...
Seite 36
... magnitudes which apply themselves exactly to one another are equal . It is here faid that AB and DE are equal . What do you understand by this word equal ? Certainly it must mean , that , if the straight lines AB and DE be properly ...
... magnitudes which apply themselves exactly to one another are equal . It is here faid that AB and DE are equal . What do you understand by this word equal ? Certainly it must mean , that , if the straight lines AB and DE be properly ...
Seite 38
... magnitudes are really equal ; and the suppofition alone is what we must truft to , for bringing this about and we are at a loss because , for this end , we begin to derive the confequences from the fuppofition before we have examined ...
... magnitudes are really equal ; and the suppofition alone is what we must truft to , for bringing this about and we are at a loss because , for this end , we begin to derive the confequences from the fuppofition before we have examined ...
Seite 50
... magnitudes , it requires fome effort of the mind to get beyond the prejudice of fenfe , fo as to comprehend the ... magnitude , instead of having recourse to fome general principles , we truft to mechanical inftruments ; and very often ...
... magnitudes , it requires fome effort of the mind to get beyond the prejudice of fenfe , fo as to comprehend the ... magnitude , instead of having recourse to fome general principles , we truft to mechanical inftruments ; and very often ...
Seite 51
... magnitudes , without being able to judge when one straight line was longer than another ; and yet it is wonderful , by how many fteps , this very teft is removed from the first principles ; and which are all neceffary for giving it a ...
... magnitudes , without being able to judge when one straight line was longer than another ; and yet it is wonderful , by how many fteps , this very teft is removed from the first principles ; and which are all neceffary for giving it a ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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.
Seite 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.
Seite 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.
Seite 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...