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 |
From inside the book
Page 82
... for inftance AB with BE , the one of which fubtends an acute angle and the other a right angle in the fame triangle . But this rectangle itself , is fufficiently or rather abfolutely determined by any two of the lines about any one of ...
... for inftance AB with BE , the one of which fubtends an acute angle and the other a right angle in the fame triangle . But this rectangle itself , is fufficiently or rather abfolutely determined by any two of the lines about any one of ...
Page 84
... fo that we have only to determine what these are according to the first definition , and then the thing propofed is ... contained in this fecond book ; it will be proper to turn his thoughts 1 . thoughts to the use which may be made of ...
... fo that we have only to determine what these are according to the first definition , and then the thing propofed is ... contained in this fecond book ; it will be proper to turn his thoughts 1 . thoughts to the use which may be made of ...
Page 86
... rectangle , the whole surface is divided into squares all equal and twenty eight in number , which is the product of four multiplied by feven . And because this parallelogram is equal to any other upon the fame or an equal base and ...
... rectangle , the whole surface is divided into squares all equal and twenty eight in number , which is the product of four multiplied by feven . And because this parallelogram is equal to any other upon the fame or an equal base and ...
Page 48
... contained by F GB , BD ; and GB is equal to A : but the rectangle DL is contained by A and DE ; for DK , that is BG ... whole line . For let the ftraight line AB be cut as it may happen in the point C I fay that the rectangle contained ...
... contained by F GB , BD ; and GB is equal to A : but the rectangle DL is contained by A and DE ; for DK , that is BG ... whole line . For let the ftraight line AB be cut as it may happen in the point C I fay that the rectangle contained ...
Page 49
... for ( by def . 1. B. 2. ) it is contained by AB , BE ; but BE is equal to BC ( being fides of a ... whole and one of the fegments , is equal to the G VOL . I. rectangle B E Book II . rectangle contained by the two segments ; OF 49 EUCLI D.
... for ( by def . 1. B. 2. ) it is contained by AB , BE ; but BE is equal to BC ( being fides of a ... whole and one of the fegments , is equal to the G VOL . I. rectangle B E Book II . rectangle contained by the two segments ; OF 49 EUCLI D.
Other editions - View all
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 conſtruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reafon fecond fegment fhall fimilar fince firſt fome fquare ftraight line AB fuch fupp fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight line BC magnitudes moſt muſt neceffary obferve parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſquare ſtraight line AC 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...