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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 26
... GKL , then as before , pro- " duce the line DA to E ; there shall AL be the line required to " be drawn from the point A equal to the given line BC . " 66 " This is the construction of the problem , " This 26 DISSERTATION II . . ...
... GKL , then as before , pro- " duce the line DA to E ; there shall AL be the line required to " be drawn from the point A equal to the given line BC . " 66 " This is the construction of the problem , " This 26 DISSERTATION II . . ...
Σελίδα 27
... construction of the problem , or the preparing of " the propofition fit for demonstration , by which you may clearly " understand the reafons of it , deduced from the few principles " already laid down : For first , that BC is equal to ...
... construction of the problem , or the preparing of " the propofition fit for demonstration , by which you may clearly " understand the reafons of it , deduced from the few principles " already laid down : For first , that BC is equal to ...
Σελίδα 29
... constructions and conclufions are alfo particular . That they are not will appear from this , that no confequence is fuppofed to follow from the ftraight lines having any particular length , nor is any construction undertaken upon that ...
... constructions and conclufions are alfo particular . That they are not will appear from this , that no confequence is fuppofed to follow from the ftraight lines having any particular length , nor is any construction undertaken upon that ...
Σελίδα 31
... constructions ; and by pro- ceeding thus you will be able to conquer the prejudice of fenfe and to acquire fomething like a scientific view of the problem . For you will find no confequence deduced from BC's having any parti- cular ...
... constructions ; and by pro- ceeding thus you will be able to conquer the prejudice of fenfe and to acquire fomething like a scientific view of the problem . For you will find no confequence deduced from BC's having any parti- cular ...
Σελίδα 33
... construction and demonstration for after shewing in what manner it may be done ; it is neceffary to prove that this is agreeable to those principles which the nature of your science obliges you to adhere to . Thus in the third ...
... construction and demonstration for after shewing in what manner it may be done ; it is neceffary to prove that this is agreeable to those principles which the nature of your science obliges you to adhere to . Thus in the third ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...