Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith1878 |
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Página vi
... magnitude capable of unlimited increase . In the Fourth Book I have made no change of importance . My treatment of the Fifth Book was suggested by the method first proposed , explained , and de- fended by Professor De Morgan in his ...
... magnitude capable of unlimited increase . In the Fourth Book I have made no change of importance . My treatment of the Fifth Book was suggested by the method first proposed , explained , and de- fended by Professor De Morgan in his ...
Página vi
... magnitude capable of unlimited increase . In the Fourth Book I have made no change of importance . My treatment of the Fifth Book was suggested by the method first proposed , explained , and de- fended by Professor De Morgan in his ...
... magnitude capable of unlimited increase . In the Fourth Book I have made no change of importance . My treatment of the Fifth Book was suggested by the method first proposed , explained , and de- fended by Professor De Morgan in his ...
Página xvii
... Magnitude is anything which is made up of parts in any way like itself . Thus , a line is a magnitude ; because we may regard it as made up of parts which are themselves lines . The properties Length , Breadth ( or Width ) , and ...
... Magnitude is anything which is made up of parts in any way like itself . Thus , a line is a magnitude ; because we may regard it as made up of parts which are themselves lines . The properties Length , Breadth ( or Width ) , and ...
Página xviii
... magnitude , since we define it as that which cannot be divided into smaller parts . II . A LINE is length without breadth . We cannot conceive a visible line without breadth ; but we can reason about lines as if they had no breadth ...
... magnitude , since we define it as that which cannot be divided into smaller parts . II . A LINE is length without breadth . We cannot conceive a visible line without breadth ; but we can reason about lines as if they had no breadth ...
Página 4
... Magnitude , inasmuch as any angle may be regarded as being made up of parts which are themselves angles . The size of an angle depends in no way on the length of the arms by which it is bounded . We shall explain hereafter the ...
... Magnitude , inasmuch as any angle may be regarded as being made up of parts which are themselves angles . The size of an angle depends in no way on the length of the arms by which it is bounded . We shall explain hereafter the ...
Términos y frases comunes
ABCD angles equal angular points base BC BC=EF bisecting the angle centre chord circumference coincide diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given point given st given straight line greater Hence inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular plane polygon PROBLEM produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained rectilinear figure reflex angle regular pentagon required to describe rhombus right angles segment semicircle shew shewn sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Pasajes populares
Página 51 - 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.
Página 5 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 38 - 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...
Página 84 - 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.
Página 165 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 104 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Página 159 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 67 - The complements of the parallelograms which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
Página 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Página 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.