The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 15
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
Σελίδα 16
... base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the equal sides are opposite ...
... base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the equal sides are opposite ...
Σελίδα 17
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1. ) ACB , the less to the great- er ; which is absurd . Therefore AB is not un- equal to AC , that is , it is equal to it . Where- fore , if two ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1. ) ACB , the less to the great- er ; which is absurd . Therefore AB is not un- equal to AC , that is , it is equal to it . Where- fore , if two ...
Σελίδα 18
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Σελίδα 19
... base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then upon the same base EF , and upon the same side of it , there can be two triangles ...
... base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then upon the same base EF , and upon the same side of it , there can be two triangles ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 81 - The angles in the same segment of a circle are equal to one another.
Σελίδα 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 22 - ANY two angles of a triangle are together less than two right angles.
Σελίδα 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Σελίδα 24 - Any two sides of a triangle are together greater than the third side.