Euclid simplified. Compiled from the most important French works, approved by the University of Paris1875 - 16 σελίδες |
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Σελίδα 5
... F. Then the angle D H A с BE G F DCB is equal to the angle HGF . For if the straight line EF be laid upon the line AB , so that the point G falls upon C , G H will take the direction CD ; otherwise , from the same point in a straight ...
... F. Then the angle D H A с BE G F DCB is equal to the angle HGF . For if the straight line EF be laid upon the line AB , so that the point G falls upon C , G H will take the direction CD ; otherwise , from the same point in a straight ...
Σελίδα 9
... point D will fall on A , and B E C A F D point E on B. But since the angle D is equal to angle A , as soon as side DE is placed on A B , side DF will take the direction A C. Moreover , DF is equal to AC ; therefore point F will fall on ...
... point D will fall on A , and B E C A F D point E on B. But since the angle D is equal to angle A , as soon as side DE is placed on A B , side DF will take the direction A C. Moreover , DF is equal to AC ; therefore point F will fall on ...
Σελίδα 10
... point B , and point F on point C. In that case , the side ED takes the direction BA , because angles DEF , ABC are equal ; side FD takes likewise the direction CA , because of the equality of angles DFE , ACB . Con- sequently point D ...
... point B , and point F on point C. In that case , the side ED takes the direction BA , because angles DEF , ABC are equal ; side FD takes likewise the direction CA , because of the equality of angles DFE , ACB . Con- sequently point D ...
Σελίδα 17
... F. half of A BF , is shorter than A C , half of ACF ; * there- fore , first , the perpendicular is shorter than ... point to a line , since it is shorter than every oblique . COROLLARY II . - From one and the same point three equal ...
... F. half of A BF , is shorter than A C , half of ACF ; * there- fore , first , the perpendicular is shorter than ... point to a line , since it is shorter than every oblique . COROLLARY II . - From one and the same point three equal ...
Σελίδα 19
... F CB , for otherwise it would be possible from point C to let drop two perpendiculars on A B. Therefore point E will fall on B , and the two triangles will perfectly coincide . * Theorem XIV . , Cor . II . THEOREM XVIII . 1. Every point ...
... F CB , for otherwise it would be possible from point C to let drop two perpendiculars on A B. Therefore point E will fall on B , and the two triangles will perfectly coincide . * Theorem XIV . , Cor . II . THEOREM XVIII . 1. Every point ...
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Euclid Simplified, Compiled from the Most Important French Works John Reynell Morell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C adjacent angles angle ABC angle BAC apotheme arc A B arithmetical mean base bisectors Book calculate chord circum circumference circumscribed coincide concave polygon convex polygon COROLLARY cumference decagon described diagonals diameter distance divide drawn equal sides equally distant equilateral triangle equivalent exterior ference geometrical locus given point given straight line greater height hexagon homologous sides hypothenuse hypothesis intersect length line BC line which joins mètres number of sides opposite sides parallel parallelogram pendicular perimeter perpendicular plane point F PROBLEM quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segments side A B side BC similar polygons similar triangles square straight line A B summit tangent Theorem VIII Theorem XIX third side trapezium triangle ABC unity
Δημοφιλή αποσπάσματα
Σελίδα 29 - 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 166 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 168 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.
Σελίδα 168 - Show that the locus of a point such that the sum of the squares of its distances from two fixed points is constant, is a circle.
Σελίδα 168 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side, plus twice the square of the median drawn to the third side.
Σελίδα 127 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 56 - BOC, inscribed in a segment less than a semicircle, is an obtuse angle ; for it is measured by half of the arc BAC, greater than a semi-circumference.
Σελίδα 1 - Things which are double of the same thing, are equal to each other. 7. Things which are halves of the same thing, are equal to each other. 8. The whole is greater than any of its parts. 9. The whole is equal to the sum of all its parts. 10. All right angles are equal to each other. II. From one point to another, only one straight line can be drawn.
Σελίδα 85 - Fig. 121. parallel to BC, the angles of the quadrilateral AEFD are equal to those of the quadrilateral ABCD; but the proportion of the sides is different. Also, without changing the four sides...
Σελίδα 101 - Scholium. The right-angled triangle is the only one in which the sum of the squares of two sides is equivalent to the square of the third ; for if the angle contained by the two sides is acute, the sum of their squares will be greater than the square of the opposite side ; if obtuse, it will be less.