Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes; together with a selection of geometrical exercises. To which is prefixed an intr., containing a brief outline of the history of geometry. By R. Potts. [With] Appendix1845 |
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Side 7
... wherefore CA , AB , BC are equal to one another : and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . From a given point , to ...
... wherefore CA , AB , BC are equal to one another : and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . From a given point , to ...
Side 8
... wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A a straight line AL ...
... wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A a straight line AL ...
Side 9
... wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would inclose a space , which is ...
... wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would inclose a space , which is ...
Side 10
... wherefore these triangles are equal , ( 1. 4. ) and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BFC to the angle CBG . And , since it ...
... wherefore these triangles are equal , ( 1. 4. ) and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BFC to the angle CBG . And , since it ...
Side 12
... wherefore the angle BDC is both equal to , and greater than the angle BCD ; which is impossible . Thirdly . The case in which the vertex of one triangle is upon a side of the other needs no demonstration . Therefore upon the same base ...
... wherefore the angle BDC is both equal to , and greater than the angle BCD ; which is impossible . Thirdly . The case in which the vertex of one triangle is upon a side of the other needs no demonstration . Therefore upon the same base ...
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Euclid's Elements of Geometry [Book 1-6, 11,12] with Explanatory Notes ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
AC is equal altitude angle ABC angle BAC angle equal base BC chord circle ABCD circumference cone cylinder describe a circle diagonals diameter divided draw EFGH equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements Geometry given angle given circle given line given point given straight line given triangle gnomon greater hypothenuse inscribed interior angles intersection isosceles triangle less Let ABC lines be drawn magnitudes meet the circumference multiple opposite sides parallel parallelogram pentagon perpendicular polygon prism problem Proclus produced Prop proportional proved pyramid Q.E.D. PROPOSITION radius rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle solid parallelopipeds square of AC tangent THEOREM touches the circle trapezium triangle ABC vertex vertical angle wherefore
Populære avsnitt
Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Side 26 - Wherefore, if a straight line, &c. QED PROPOSITION XXIX. THEOREM. Jf a straight line fall upon two parallel straight lines, it makes the alternate angles equal...
Side 99 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Side 58 - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 22 - IF two triangles have two sides of the one equal to two sides of the...
Side vi - The sluggard is wiser in his own conceit than seven men that can render a reason.
Side 54 - If there be imo 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.
Side 26 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.