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 |
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Side 19
B с F G The three sides of the triangle ABG are AG , AB , BG and the three angles
are ABG , AGB , GAB : and of the triangle ACF the three sides are AF , AC , CF i
and the three angles ACF , AFC , CAF and the angle at A or DAE is said to be ...
B с F G The three sides of the triangle ABG are AG , AB , BG and the three angles
are ABG , AGB , GAB : and of the triangle ACF the three sides are AF , AC , CF i
and the three angles ACF , AFC , CAF and the angle at A or DAE is said to be ...
Side 35
But to be more particular , Let ABC and DEF be two A triangles ; having the two
fides AB and AC equal to the two sides DE and DF ; each to each , viz . the side
AB equal to DE ; and the side AC equal to DF ; and the B с Е F angle contained
by ...
But to be more particular , Let ABC and DEF be two A triangles ; having the two
fides AB and AC equal to the two sides DE and DF ; each to each , viz . the side
AB equal to DE ; and the side AC equal to DF ; and the B с Е F angle contained
by ...
Side 37
... will then take a direction , on the one side or the other of DF , according as the
angle BAC is greater or less than EDF . ... will carry us a step beyond the
common sense of mankind : for he who first found out that the two sides , and
included ...
... will then take a direction , on the one side or the other of DF , according as the
angle BAC is greater or less than EDF . ... will carry us a step beyond the
common sense of mankind : for he who first found out that the two sides , and
included ...
Side 43
the steps of the demonstration ; but as carrying with it this extensive and general
meaning , that all triangles which have two sides equal to two sides , each to
each , and the angles , contained by those sides , equal ; that all such triangles , I
...
the steps of the demonstration ; but as carrying with it this extensive and general
meaning , that all triangles which have two sides equal to two sides , each to
each , and the angles , contained by those sides , equal ; that all such triangles , I
...
Side 44
... the inclination of the lines , and the length of the sides , climb up by degrees to
something like a scientific conception of its meaning . The other two triangles
FBC and CGB , though they represent a particular instance of the fourth
proposition ...
... the inclination of the lines , and the length of the sides , climb up by degrees to
something like a scientific conception of its meaning . The other two triangles
FBC and CGB , though they represent a particular instance of the fourth
proposition ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD added alſo angle BAC angle contained angle equal apply baſe BC is equal becauſe Book called certainly circle circle ABC circumference conſequences conſider conſtruction definition demonſtrated deſcribed diameter double drawn equal equal angles equiangular equilateral equimultiples Euclid examination exceed fall fame fides figure firſt follow fore four fourth given greater happen hath itſelf joined leſs magnitudes means meet multiple muſt parallel parallelogram particular principles produced prop properties proportionals propoſition prove reader reaſon rectangle contained rectilineal figure remaining angle right angles ſaid ſame ſame multiple ſame ratio ſay ſecond ſegment ſhall ſides ſimilar ſome ſquare ſtraight line BC ſuch ſuppoſe ſuppoſition taken theſe thing third thoſe touch triangle ABC uſe wherefore whole
Populære avsnitt
Side 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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...
Side 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.
Side 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.
Side 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.
Side 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.
Side 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...
Bibliografisk informasjon
| Tittel | 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 Volum 1 av 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. Vol. I, Oxford University Press |
| Forfattere | Euclid, James Williamson |
| Bidragsyter | Oxford University Press |
| Utgiver | Printed at the Clarendon Press, 1781 |
| Original fra | Oxford University |
| Digitalisert | 29. aug 2007 |
| Lengde | 309 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |