Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of SolidsF. Nichols, 1806 - 311 σελίδες |
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Σελίδα 3
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XIV . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . Book ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XIV . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . Book ...
Σελίδα 35
... diameter bisects it , that is , divides it into two equal parts . : N. B. A parallelogram is a four sided figure , of which the opposite sides are parallel ; and the diame- ter is the straight line joining two of its opposite angles ...
... diameter bisects it , that is , divides it into two equal parts . : N. B. A parallelogram is a four sided figure , of which the opposite sides are parallel ; and the diame- ter is the straight line joining two of its opposite angles ...
Σελίδα 36
... diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal to the triangle BCD , and ...
... diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal to the triangle BCD , and ...
Σελίδα 38
... diameter AB bisects it ; and the triangle DBC is the half of the parallelogram DBCF ; therefore the triangle ABC is equald to the triangle DBC . Wherefore , triangles , & c . Q. E. D. PROP . XXXVIII . THEOR . TRIANGLES upon equal bases ...
... diameter AB bisects it ; and the triangle DBC is the half of the parallelogram DBCF ; therefore the triangle ABC is equald to the triangle DBC . Wherefore , triangles , & c . Q. E. D. PROP . XXXVIII . THEOR . TRIANGLES upon equal bases ...
Σελίδα 42
... diameter of any parallelogram are equal to one another . Let ABCD be a parallelogram , of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other paral ...
... diameter of any parallelogram are equal to one another . Let ABCD be a parallelogram , of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other paral ...
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ABC is equal altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide common section cylinder definition demonstrated diameter draw drawa equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fore four right angles given circle given straight line greater inscribed interior and opposite join less Let ABC Let the straight meet multiple opposite angle parallelogram parallelogram ABCD perpendicular point F polygon prism PROB produced proportional proposition pyramid Q. E. D. COR Q. E. D. PROP ratio rectangle contained rectilineal figure remaining angle segment solid angle solid parallelepipeds straight line AB straight line AC Suppl THEOR third touches the circle triangle ABC triangle DEF
Δημοφιλή αποσπάσματα
Σελίδα 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 3 - 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.
Σελίδα 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 291 - 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 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Σελίδα 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Σελίδα 14 - Therefore, 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 extretnity equal to one another.