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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Αποτελέσματα 6 - 10 από τα 100.
Σελίδα 35
... figure CEFG is a parallelogram . ( def . A. ) And because the triangles ABE , AEC are on the equal bases BE , EC , and between the same parallels BC , AG ; they are therefore equal to one another ; ( 1. 38. ) and therefore the triangle ...
... figure CEFG is a parallelogram . ( def . A. ) And because the triangles ABE , AEC are on the equal bases BE , EC , and between the same parallels BC , AG ; they are therefore equal to one another ; ( 1. 38. ) and therefore the triangle ...
Σελίδα 37
... figure , and having an angle equal to a given rectilineal angle . Let ABCD be the given rectilineal figure , and E the given rec◅ tilineal angle . It is required to describe a parallelogram that shall be equal to the figure ABCD , and ...
... figure , and having an angle equal to a given rectilineal angle . Let ABCD be the given rectilineal figure , and E the given rec◅ tilineal angle . It is required to describe a parallelogram that shall be equal to the figure ABCD , and ...
Σελίδα 38
... figure ABCD , having the angle FKM equal to the given angle E. Q. E. F. COR . From this it is manifest how , to a ... figure ; viz . by applying to the given straight line a parallelogram equal to the first triangle ABD , ( 1.44 . ) and ...
... figure ABCD , having the angle FKM equal to the given angle E. Q. E. F. COR . From this it is manifest how , to a ... figure ; viz . by applying to the given straight line a parallelogram equal to the first triangle ABD , ( 1.44 . ) and ...
Σελίδα 43
... figure , as in certain conic lines . " Def . XXIV - XXIX . Triangles are divided into three classes by reference to ... figure having all its sides equal , and one angle a right angle : because it is proved in Prop . 46 , Book 1 , that ...
... figure , as in certain conic lines . " Def . XXIV - XXIX . Triangles are divided into three classes by reference to ... figure having all its sides equal , and one angle a right angle : because it is proved in Prop . 46 , Book 1 , that ...
Σελίδα 45
... figure is conceived to be placed upon another , so that the boundaries of one exactly coincide with the boundaries of the other , then the two plane figures are equal . It may also be remarked , that the converse of this proposition is ...
... figure is conceived to be placed upon another , so that the boundaries of one exactly coincide with the boundaries of the other , then the two plane figures are equal . It may also be remarked , that the converse of this proposition is ...
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.