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 1 - 5 από τα 100.
Σελίδα 10
... equal to the base GB , ( 1. 4. ) and the triangle AFC is equal to the triangle AGB , also the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the ...
... equal to the base GB , ( 1. 4. ) and the triangle AFC is equal to the triangle AGB , also the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the ...
Σελίδα 13
... equal angles . Let BAC be the given rectilineal angle . It is required to bisect it . A D E Take any point D in AB ; from AC cut off AE equal to AD ; ( 1. 3. ) and join DE , describe an equilateral triangle DEF on the side of DE remote ...
... equal angles . Let BAC be the given rectilineal angle . It is required to bisect it . A D E Take any point D in AB ; from AC cut off AE equal to AD ; ( 1. 3. ) and join DE , describe an equilateral triangle DEF on the side of DE remote ...
Σελίδα 16
Euclides Robert Potts. Again , because the angle DBA is equal to the two angles DBE , EBA , add to each of these equals the angle ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC . But the angles CBE ...
Euclides Robert Potts. Again , because the angle DBA is equal to the two angles DBE , EBA , add to each of these equals the angle ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC . But the angles CBE ...
Σελίδα 23
... equal to the two sides DE , DF , each to each , namely , AB equal to DE , and AC to DF ; but the base BC greater than the base EF . Then the angle BAC shall be greater than the angle EDF . A D B C E F For , if the angle BAC be not ...
... equal to the two sides DE , DF , each to each , namely , AB equal to DE , and AC to DF ; but the base BC greater than the base EF . Then the angle BAC shall be greater than the angle EDF . A D B C E F For , if the angle BAC be not ...
Σελίδα 24
... equal to ED , ( 1. 3. ) and join GC . Then in the two triangles GBC , DEF , because GB is equal to DE , and BC to EF ... angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal ...
... equal to ED , ( 1. 3. ) and join GC . Then in the two triangles GBC , DEF , because GB is equal to DE , and BC to EF ... angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal ...
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.