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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Σελίδα xiii
... similar sections of the cone . Book VII . contains a collection of Theorems useful in the solution of Problems . Book VIII . was a collection of Problems with their solutions by means of the Theorems in Book VII . Besides the treatise ...
... similar sections of the cone . Book VII . contains a collection of Theorems useful in the solution of Problems . Book VIII . was a collection of Problems with their solutions by means of the Theorems in Book VII . Besides the treatise ...
Σελίδα 50
... similar objection , being the converse of Prop . 27 , Book 1 . Professor Playfair has adopted in his Elements of Geometry , that " Two straight lines which intersect one another cannot be both parallel to the same straight line . " This ...
... similar objection , being the converse of Prop . 27 , Book 1 . Professor Playfair has adopted in his Elements of Geometry , that " Two straight lines which intersect one another cannot be both parallel to the same straight line . " This ...
Σελίδα 68
... similar manner , that the area of the rectangle AC would contain ab square units ; and therefore the product ab is a proper representation for the area of the rectangle AC . Hence , it follows , that the term rectangle in Geometry ...
... similar manner , that the area of the rectangle AC would contain ab square units ; and therefore the product ab is a proper representation for the area of the rectangle AC . Hence , it follows , that the term rectangle in Geometry ...
Σελίδα 94
... similar to the segment ADB , ( hyp . ) and that similar segments of circles contain equal angles ; ( III . def . 11. ) therefore the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible . ( 1. 16 ...
... similar to the segment ADB , ( hyp . ) and that similar segments of circles contain equal angles ; ( III . def . 11. ) therefore the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible . ( 1. 16 ...
Σελίδα 96
... similar to the segment EDF ; ( III . def . 11. ) and they are upon equal straight lines BC , ÈF : but similar segments of circles upon equal straight lines , are equal to one another , ( 111. 24. ) therefore the segment BAC is equal to ...
... similar to the segment EDF ; ( III . def . 11. ) and they are upon equal straight lines BC , ÈF : but similar segments of circles upon equal straight lines , are equal to one another , ( 111. 24. ) therefore the segment BAC is equal to ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry [Book 1-6, 11,12] with Explanatory Notes ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 22 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα vi - The sluggard is wiser in his own conceit than seven men that can render a reason.
Σελίδα 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.
Σελίδα 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.