The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 10.
Σελίδα 2
An acute angle is that which is less than a right angle . Acute . Obtuse . XIII . A
term or boundary is the extremity of any thing . XIV . A figure is that which is
enclosed by one or more boundaries . XV . A circle is a plain figure contained by
one line ...
An acute angle is that which is less than a right angle . Acute . Obtuse . XIII . A
term or boundary is the extremity of any thing . XIV . A figure is that which is
enclosed by one or more boundaries . XV . A circle is a plain figure contained by
one line ...
Σελίδα 8
Upon the same base , and on the same side of it , there cannot be two triangles
that have their sides which are terminated in one extremity of the base equal to
one another , and likewise those which are terminated in the other extremity . If it
be ...
Upon the same base , and on the same side of it , there cannot be two triangles
that have their sides which are terminated in one extremity of the base equal to
one another , and likewise those which are terminated in the other extremity . If it
be ...
Σελίδα 9
... and upon the same side of it , there can be two triangles that have their sides
which are terminated in one extremity of the base equal to one another , and
likewise their sides terminated in the other extremity ; but this is impossible ( i .
... and upon the same side of it , there can be two triangles that have their sides
which are terminated in one extremity of the base equal to one another , and
likewise their sides terminated in the other extremity ; but this is impossible ( i .
Σελίδα 58
Wherefore the diameter , & c . Q . E . D . PROPOSITION XVI . — THEOREM , The
straight line drawn at right angles to the diameter of a circle , from the extremity of
it , falls without the circle ; and no straight line can be drawn between that ...
Wherefore the diameter , & c . Q . E . D . PROPOSITION XVI . — THEOREM , The
straight line drawn at right angles to the diameter of a circle , from the extremity of
it , falls without the circle ; and no straight line can be drawn between that ...
Σελίδα 59
From this it is manifest , that the straight line which is drawn at right angles to the
diameter of a circle from the extremity of it , touches the circle ; and that it touches
it only in one point , because if it did meet the circle in two , it would fall within it ...
From this it is manifest , that the straight line which is drawn at right angles to the
diameter of a circle from the extremity of it , touches the circle ; and that it touches
it only in one point , because if it did meet the circle in two , it would fall within it ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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Συχνά εμφανιζόμενοι όροι και φράσεις
a b c angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore fourth given rectilineal given straight line greater half inscribed join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Σελίδα 42 - 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 of the other part.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 21 - 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.
Σελίδα 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 38 - 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 of...
Σελίδα 15 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 126 - 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.