The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 σελίδες |
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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 10
... fore also the point C shall coincide with the point F , because ( hyp . ) AC is equal to DF . But the point B coincides with E ; wherefore the base BC shall coincide with the base EF ; because , the point B coinciding with E , and C ...
... fore also the point C shall coincide with the point F , because ( hyp . ) AC is equal to DF . But the point B coincides with E ; wherefore the base BC shall coincide with the base EF ; because , the point B coinciding with E , and C ...
Σελίδα 11
... fore the angle AFC is equal to the angle AGB . And because the whole AF is equal ( const . ) to the D whole AG , of which the parts AB , AC are ( hyp . ) equal ; the remainder BF is equal ( I. ax . 3 ) to the remainder CG ; and FC has ...
... fore the angle AFC is equal to the angle AGB . And because the whole AF is equal ( const . ) to the D whole AG , of which the parts AB , AC are ( hyp . ) equal ; the remainder BF is equal ( I. ax . 3 ) to the remainder CG ; and FC has ...
Σελίδα 20
... fore , is not less than AB ; and it has been shown that it is not equal to AB : therefore AC is greater than AB . Wherefore , if two angles , & c . B PROP . XX . THEOR . - Any two sides of a triangle are to- gether greater than the ...
... fore , is not less than AB ; and it has been shown that it is not equal to AB : therefore AC is greater than AB . Wherefore , if two angles , & c . B PROP . XX . THEOR . - Any two sides of a triangle are to- gether greater than the ...
Σελίδα 21
... fore CE , EB are greater than CD , DB . But it has been shown that BA , AC are greater than BE , EC : much more then are BA , AC greater than BD , DC . B Again , the exterior angle BDC of the triangle CDE is greater ( I. 16 ) than CED ...
... fore CE , EB are greater than CD , DB . But it has been shown that BA , AC are greater than BE , EC : much more then are BA , AC greater than BD , DC . B Again , the exterior angle BDC of the triangle CDE is greater ( I. 16 ) than CED ...
Σελίδα 24
... fore , if two triangles , & c . PROP . XXVI . THEOR . - If two angles of one triangle be equal to two angles of another , each to each , and if a side of the one be equal to a side of the other similarly situated with respect to those ...
... fore , if two triangles , & c . PROP . XXVI . THEOR . - If two angles of one triangle be equal to two angles of another , each to each , and if a side of the one be equal to a side of the other similarly situated with respect to those ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 130 - 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 45 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 7 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 27 - 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 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.