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 7
... shew hereafter , be deduced from a more simple Postulate . The student must defer the consideration of this Postulate , till he has reached the 17th Proposition of Book I. Euclid next enumerates , as statements of fact , nine Axioms or ...
... shew hereafter , be deduced from a more simple Postulate . The student must defer the consideration of this Postulate , till he has reached the 17th Proposition of Book I. Euclid next enumerates , as statements of fact , nine Axioms or ...
Página 20
... Shew that we can prove this Proposition by means of Prop . IV . and PROP . A. , without applying Prop . C. Ex . 2. If the equilateral triangle , employed in the construc- tion , be described with its vertex towards the given angle ; shew ...
... Shew that we can prove this Proposition by means of Prop . IV . and PROP . A. , without applying Prop . C. Ex . 2. If the equilateral triangle , employed in the construc- tion , be described with its vertex towards the given angle ; shew ...
Página 22
... Shew that in the diagram of Prop . ix . AF and ED intersect each other at right angles , and that ED is bisected by ... shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular case of Prop . IX . PROPOSITION ...
... Shew that in the diagram of Prop . ix . AF and ED intersect each other at right angles , and that ED is bisected by ... shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular case of Prop . IX . PROPOSITION ...
Página 24
... shew that BDC is an isosceles triangle . 4. D , E , F are points taken in the sides BC , CA , AB , of an equilateral triangle , so that BD = CE = AF . Shew that the triangle DEF is equilateral . 5. In a given straight line find a point ...
... shew that BDC is an isosceles triangle . 4. D , E , F are points taken in the sides BC , CA , AB , of an equilateral triangle , so that BD = CE = AF . Shew that the triangle DEF is equilateral . 5. In a given straight line find a point ...
Página 25
... Shew that the angles at O are together equal to four right angles . NOTE ( 1. ) If two angles together make up a right angle , each is called the COMPLEMENT of the other . Thus , in fig . 2 , △ ABD is the complement of △ ABE . ( 2 ...
... Shew that the angles at O are together equal to four right angles . NOTE ( 1. ) If two angles together make up a right angle , each is called the COMPLEMENT of the other . Thus , in fig . 2 , △ ABD is the complement of △ ABE . ( 2 ...
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.