Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 σελίδες |
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Σελίδα iii
... book of Elementary Geometry is still con- sidered as the best , and that the writings of EUCLID , at the distance of two thousand years , continue to form the most approved introduction to the mathema- tical sciences . This remarkable ...
... book of Elementary Geometry is still con- sidered as the best , and that the writings of EUCLID , at the distance of two thousand years , continue to form the most approved introduction to the mathema- tical sciences . This remarkable ...
Σελίδα vi
... book , they seem to arise chiefly from the nature of the language employed , which being no other than that of ... Book , than those of any other of the Elements . In the Second Book , also , some algebraic signs have been ...
... book , they seem to arise chiefly from the nature of the language employed , which being no other than that of ... Book , than those of any other of the Elements . In the Second Book , also , some algebraic signs have been ...
Σελίδα vii
... Book , and particu- larly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third Book , the remarks con ...
... Book , and particu- larly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third Book , the remarks con ...
Σελίδα ix
... Book of the Supplement , which treats of the intersection of Planes , I have departed as little as possible from EUCLID'S method of consi- dering the same subject in his eleventh Book . The demonstration of the fourth proposition is ...
... Book of the Supplement , which treats of the intersection of Planes , I have departed as little as possible from EUCLID'S method of consi- dering the same subject in his eleventh Book . The demonstration of the fourth proposition is ...
Σελίδα xi
... Book , therefore , on the Properties of Solids , which I now offer to the public , I have not sought to subject the demonstrations to the law just mentioned , and have never hesitated to admit the existence of such solids , or such ...
... Book , therefore , on the Properties of Solids , which I now offer to the public , I have not sought to subject the demonstrations to the law just mentioned , and have never hesitated to admit the existence of such solids , or such ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...
Σελίδα 19 - 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 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 292 - 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 308 - 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 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.