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 51
... ABCD is equal to the parallelogram EBCF . Other wise , the triangle , whose base is DE , ( fig . 2. ) is taken twice ... circle , the two most simple loci ; all other loci , perhaps including also the Conic Sections , may be more readily ...
... ABCD is equal to the parallelogram EBCF . Other wise , the triangle , whose base is DE , ( fig . 2. ) is taken twice ... circle , the two most simple loci ; all other loci , perhaps including also the Conic Sections , may be more readily ...
Página 79
... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ... circle , ( 111. 1. ) and join EF . Then because FE , a straight line drawn through the centre , bisects another AC ...
... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ... circle , ( 111. 1. ) and join EF . Then because FE , a straight line drawn through the centre , bisects another AC ...
Página 81
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre : let the centre be E. Then , of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA , that in ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre : let the centre be E. Then , of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA , that in ...
Página 88
... circle ; and , of all others , that which is nearer to the centre is always greater than one more remote : and the greater is nearer to the centre than the less . Let ABCD be a circle , of which the diameter is AD , and the centre E ...
... circle ; and , of all others , that which is nearer to the centre is always greater than one more remote : and the greater is nearer to the centre than the less . Let ABCD be a circle , of which the diameter is AD , and the centre E ...
Página 93
... circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED . Then the angles BAD , BED shall be equal to one another . First , let the segment BAED be greater than a semicircle . E B C Take F ...
... circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED . Then the angles BAD , BED shall be equal to one another . First , let the segment BAED be greater than a semicircle . E B C Take F ...
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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.