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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Página iii
... shewn from the seventh book of the Republic of Plato . To his testimony may be added that of the celebrated Pascal , ( Euvres , Tom . I. p . 66 , ) which Mr Hallam has quoted in his History of the Literature of the Middle Ages ...
... shewn from the seventh book of the Republic of Plato . To his testimony may be added that of the celebrated Pascal , ( Euvres , Tom . I. p . 66 , ) which Mr Hallam has quoted in his History of the Literature of the Middle Ages ...
Página vi
... shewn , in his Thoughts on the Study of Mathematics , " that mathematical studies judiciously pursued , form one of the most effective means of developing and cultivating the reason : and that " the object of a liberal education is to ...
... shewn , in his Thoughts on the Study of Mathematics , " that mathematical studies judiciously pursued , form one of the most effective means of developing and cultivating the reason : and that " the object of a liberal education is to ...
Página xvii
... shewn that there can be only five regular solids , or that only equi- lateral triangles , squares , and pentagons , can form the boundaries of regular solid bodies . The sixth book is employed chiefly in explaining and connecting some ...
... shewn that there can be only five regular solids , or that only equi- lateral triangles , squares , and pentagons , can form the boundaries of regular solid bodies . The sixth book is employed chiefly in explaining and connecting some ...
Página 27
... shewn that the angle AGH is equal to the angle GHF ; therefore the angle AGH is equal to the angle GKD ; and these are alternate angles ; therefore AB is parallel to CD . ( 1. 27. ) Wherefore straight lines which are , & c . PROPOSITION ...
... shewn that the angle AGH is equal to the angle GHF ; therefore the angle AGH is equal to the angle GKD ; and these are alternate angles ; therefore AB is parallel to CD . ( 1. 27. ) Wherefore straight lines which are , & c . PROPOSITION ...
Página 28
... shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : ( ax . 2. ) to each of these equals add the angle ACB , therefore the angles ACD and ACB are equal ...
... shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : ( ax . 2. ) to each of these equals add the angle ACB , therefore the angles ACD and ACB are equal ...
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Euclid's Elements of Geometry [Book 1-6, 11,12] with Explanatory Notes ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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.
Página 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...
Página 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.
Página 22 - IF two triangles have two sides of the one equal to two sides of the...
Página vi - The sluggard is wiser in his own conceit than seven men that can render a reason.
Página 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.
Página 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.