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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Σελίδα 15
... containing an angle . This plane rectilineal angle may be of three different kinds ; according to the different ... angles with the other , on each fide one . Turn the pens into the fame direction , and making one of them revolve , and ...
... containing an angle . This plane rectilineal angle may be of three different kinds ; according to the different ... angles with the other , on each fide one . Turn the pens into the fame direction , and making one of them revolve , and ...
Σελίδα 19
... contained by the fides FA , AC when it is confidered as an angle of the triangle ACF : but when it is confidered as an angle of the triangle ABG it is said to be contained by GA , AB . F D B A C G E and the Again FBC and BCG are alfo ...
... contained by the fides FA , AC when it is confidered as an angle of the triangle ACF : but when it is confidered as an angle of the triangle ABG it is said to be contained by GA , AB . F D B A C G E and the Again FBC and BCG are alfo ...
Σελίδα 22
... Containing an explanation of the two first propofitions . THE two firft ... contains " therefore and shews a double invention , without which or some ' " fuch ... angle , that is not yet known , and fome inven- " tion must be thought of ...
... Containing an explanation of the two first propofitions . THE two firft ... contains " therefore and shews a double invention , without which or some ' " fuch ... angle , that is not yet known , and fome inven- " tion must be thought of ...
Σελίδα 35
... angle contained by BAC equal to the angle contained by EDF . B CE F This now is the hypothefis or fuppofition , which is to be con- fidered as abfolutely certain ; and a principle from which we are to reason as confidently , as from the ...
... angle contained by BAC equal to the angle contained by EDF . B CE F This now is the hypothefis or fuppofition , which is to be con- fidered as abfolutely certain ; and a principle from which we are to reason as confidently , as from the ...
Σελίδα 40
... angle equal to the angle at the vertex of the ifofceles triangle , this angle must be made , which , in our prefent circumftances , will not be found fuch an eafy matter . And so much for hypotheses or suppositions . СНАР . V. Containing ...
... angle equal to the angle at the vertex of the ifofceles triangle , this angle must be made , which , in our prefent circumftances , will not be found fuch an eafy matter . And so much for hypotheses or suppositions . СНАР . V. Containing ...
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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...