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 xxxi
... similar triangles are proportionals ; and in right - angled triangles the square of the hypothenuse is equal to the squares of the two sides . And I am not afraid to suppose several unknown quantities , that I may reduce the proposed ...
... similar triangles are proportionals ; and in right - angled triangles the square of the hypothenuse is equal to the squares of the two sides . And I am not afraid to suppose several unknown quantities , that I may reduce the proposed ...
Σελίδα 31
... same parallels , are equal to one another . Let the parallelograms ABCD , EBCF be ... similar reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1 ... triangles EAB , FDC , because FD is equal to EA , and DC to AB , and the ...
... same parallels , are equal to one another . Let the parallelograms ABCD , EBCF be ... similar reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1 ... triangles EAB , FDC , because FD is equal to EA , and DC to AB , and the ...
Σελίδα 32
... triangle DBC . Wherefore triangles , & c . Q. E.D. PROPOSITION XXXVIII . THEOREM . Triangles upon equal bases , and between the same parallels , are equal to one another . Let the triangles ABC , DEF be upon equal bases 32 EUCLID'S ELEMENTS ...
... triangle DBC . Wherefore triangles , & c . Q. E.D. PROPOSITION XXXVIII . THEOREM . Triangles upon equal bases , and between the same parallels , are equal to one another . Let the triangles ABC , DEF be upon equal bases 32 EUCLID'S ELEMENTS ...
Σελίδα 43
... triangle are acute , which is supposed in Def . 29. It may be replied , that the definitions of the three kinds of angles point out and seem to supply a foundation for a similar distinction of triangles . Def . XXX - XXXIV . The ...
... triangle are acute , which is supposed in Def . 29. It may be replied , that the definitions of the three kinds of angles point out and seem to supply a foundation for a similar distinction of triangles . Def . XXX - XXXIV . The ...
Σελίδα 95
... equal to CD : therefore , the straight line AB coinciding with CD , the segment AEB must coincide with the segment CFD , ( 111. 23. ) and therefore is equal to it . ( ax . 8. ) Wherefore similar ... triangles ADE , CDE , the two sides AD , DE ...
... equal to CD : therefore , the straight line AB coinciding with CD , the segment AEB must coincide with the segment CFD , ( 111. 23. ) and therefore is equal to it . ( ax . 8. ) Wherefore similar ... triangles ADE , CDE , the two sides AD , DE ...
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.