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 9
... sides of the one equal to two sides , & c . Which was to be demonstrated . PROPOSITION V. THEOREM . The angles at the base of an isosceles triangle are equal to each other ; and if the equal sides be produced , the angles on the other side ...
... sides of the one equal to two sides , & c . Which was to be demonstrated . PROPOSITION V. THEOREM . The angles at the base of an isosceles triangle are equal to each other ; and if the equal sides be produced , the angles on the other side ...
Σελίδα 10
... sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB . And because the whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; therefore the remainder BF is equal to the ...
... sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB . And because the whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; therefore the remainder BF is equal to the ...
Σελίδα 12
... sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angles con- tained by the two sides equal to them ...
... sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angles con- tained by the two sides equal to them ...
Σελίδα 19
... side . Let ABC be a triangle . Then any two sides of it together shall be greater than the third side , viz . the sides BA , AC greater than the side BC ; AB , BC greater than AC ; and BC , CA greater than AB . B A D Produce the side BA ...
... side . Let ABC be a triangle . Then any two sides of it together shall be greater than the third side , viz . the sides BA , AC greater than the side BC ; AB , BC greater than AC ; and BC , CA greater than AB . B A D Produce the side BA ...
Σελίδα 20
... side BC ; but DB is equal to BA and AC , therefore the sides BÃ and AC are greater than BC . In the same manner it may be demonstrated , that the sides AB , BC are greater than CA ; also that BC , CA are greater than AB . Therefore any two ...
... side BC ; but DB is equal to BA and AC , therefore the sides BÃ and AC are greater than BC . In the same manner it may be demonstrated , that the sides AB , BC are greater than CA ; also that BC , CA are greater than AB . Therefore any two ...
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.