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 8
... ABC is equal to ACB . CHAP . IV . In what manner our common notions begin to take a Scientific form . AFTER the ... circle whose radius is a thousand miles , or the thousand part of an inch , would furnish the same conclufions as ...
... ABC is equal to ACB . CHAP . IV . In what manner our common notions begin to take a Scientific form . AFTER the ... circle whose radius is a thousand miles , or the thousand part of an inch , would furnish the same conclufions as ...
Seite 23
... circle then will give you a line , in which are contained " all the points or ends of the infinite lines , which may ... ABC ; which was desired . This is " the first part of the pro- " blem , and indeed the difficultest to find ...
... circle then will give you a line , in which are contained " all the points or ends of the infinite lines , which may ... ABC ; which was desired . This is " the first part of the pro- " blem , and indeed the difficultest to find ...
Seite 24
... circle , he chuses rather to " make use of an equilateral triangle to find out that propriety of ** a point so ... ABC bounded and limited by " them is an equilateral triangle , according to the description of " that figure in the ...
... circle , he chuses rather to " make use of an equilateral triangle to find out that propriety of ** a point so ... ABC bounded and limited by " them is an equilateral triangle , according to the description of " that figure in the ...
Seite 26
... ABC was an equilateral triangle ; and there could be but " two fuch made upon the line AB in the fame plain ; there being " but two points where in those circles cut each other ; those cir- " cles determining all the lines equal to AB ...
... ABC was an equilateral triangle ; and there could be but " two fuch made upon the line AB in the fame plain ; there being " but two points where in those circles cut each other ; those cir- " cles determining all the lines equal to AB ...
Seite 54
... ABC to be equal to DCB . I would recommend the performance of such con- structions as this , by the hand unguided by ... circle cut AB in some such point as D ; be- cause the whole construction will be necessary to convince the ...
... ABC to be equal to DCB . I would recommend the performance of such con- structions as this , by the hand unguided by ... circle cut AB in some such point as D ; be- cause the whole construction will be necessary to convince the ...
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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 alſo alſo equal angle ABC angle BAC angle contained angle equal apply itſelf baſe BC is equal Book certainly circle ABC circumference common notion conſequences conſtruction cut in halves demonſtrated deſcribed diſtance drawn equal angles equal ſtraight lines equiangular equilateral equimultiples Euclid exceed fame fides firſt given rectilineal given ſtraight line greater hath inſcribe inſtance inſtruments joined leſs let the ſtraight magnitudes moſt muſt neceſſary obſerve oppoſite parallelogram poſition PROP proportionals propoſition purpoſe reader reaſon alſo rectangle contained rectilineal figure remaining angle right angles ſaid ſame manner ſame multiple ſame ratio ſame reaſon ſay ſcience ſecond ſector ſegment ſenſe ſhall ſhould ſide ſimilar ſome ſquare ſquare of AC ſtand ſtraight line AB straight line BC ſtudent ſubject ſuch ſupp ſuppoſe ſuppoſition taken theſe thoſe tiple triangle ABC 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...