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 27
... reasons of it , deduced from the few principles " already laid down : For first , that BC is equal to BG is ... also by the construction equal to BG ; " therefore fince by the first axiom these two quantities which are " equal ...
... reasons of it , deduced from the few principles " already laid down : For first , that BC is equal to BG is ... also by the construction equal to BG ; " therefore fince by the first axiom these two quantities which are " equal ...
Seite 34
... also have the base equal to the base ; and the triangle will be equal to the triangle ; and the remaining angles ... reason accurately from a suppo- sition is no easy matter ; attention and habit will do a great deal , but above ...
... also have the base equal to the base ; and the triangle will be equal to the triangle ; and the remaining angles ... reason accurately from a suppo- sition is no easy matter ; attention and habit will do a great deal , but above ...
Seite 35
... reason as confidently , as from the first common notion that mag- nitudes , equal to the fame , are equal to one ... also have the third fide or base BC equal to the bafe EF ; and the whole triangle ABC equal to the whole triangle ...
... reason as confidently , as from the first common notion that mag- nitudes , equal to the fame , are equal to one ... also have the third fide or base BC equal to the bafe EF ; and the whole triangle ABC equal to the whole triangle ...
Seite 36
... also fixed ; because they are to have the lines which are equal by the supposition extended under them ; that is the ... too much for the learner to attempt the whole demonstration at once ; let us therefore fee what consequence ...
... also fixed ; because they are to have the lines which are equal by the supposition extended under them ; that is the ... too much for the learner to attempt the whole demonstration at once ; let us therefore fee what consequence ...
Seite 43
... too complicated for this purpose ; because not only DE and DF were to be equal to each other and to AB and AC , for this might have been al- lowed ; but also the angles between the sides were to be equal , which could by no means be ...
... too complicated for this purpose ; because not only DE and DF were to be equal to each other and to AB and AC , for this might have been al- lowed ; but also the angles between the sides were to be equal , which could by no means be ...
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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...