Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith1876 - 349 páginas |
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Página 4
... whole , of which the parts are the angles AOB , BOC , and COD . Hence we may regard an angle as a 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 ...
... whole , of which the parts are the angles AOB , BOC , and COD . Hence we may regard an angle as a 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 ...
Página 8
... whole is greater than its part . With his Common Notions Euclid takes the ground of authority , saying in effect , " To my Postulates I request , to my Common Notions I claim , your assent . " Euclid develops the science of Geometry in ...
... whole is greater than its part . With his Common Notions Euclid takes the ground of authority , saying in effect , " To my Postulates I request , to my Common Notions I claim , your assent . " Euclid develops the science of Geometry in ...
Página 19
... whole angles BAD , BDA are equal . I. A. Ax . 3 . and parts of these CAD , CDA are equal . .. the remainders BAC , BDC are equal . Then , as in Case I. , the equality of the original triangles may be proved . CASE III . When AC and CD ...
... whole angles BAD , BDA are equal . I. A. Ax . 3 . and parts of these CAD , CDA are equal . .. the remainders BAC , BDC are equal . Then , as in Case I. , the equality of the original triangles may be proved . CASE III . When AC and CD ...
Página 19
... finite straight line to a point , such that the part produced may be one - third of the line , which is made up of the whole and the part produced . PROPOSITION IX . PROBLEM . To bisect a given angle Book L1 23 PROPOSITION XII .
... finite straight line to a point , such that the part produced may be one - third of the line , which is made up of the whole and the part produced . PROPOSITION IX . PROBLEM . To bisect a given angle Book L1 23 PROPOSITION XII .
Página 21
... finite straight line to a point , such that the part produced may be one - third of the line , which is made up of the whole and the part produced . PROPOSITION XI . PROBLEM . To draw a straight line Book I.J 21 PROPOSITION X. ང.
... finite straight line to a point , such that the part produced may be one - third of the line , which is made up of the whole and the part produced . PROPOSITION XI . PROBLEM . To draw a straight line Book I.J 21 PROPOSITION X. ང.
Otras ediciones - Ver todas
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Sin vista previa disponible - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Sin vista previa disponible - 2018 |
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 equal circles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater than nD Hence inscribed isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius rectangle contained reflex angle required to describe rhombus right angles segment semicircle shew shewn straight line joining subtended 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 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 178 - 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 46 - 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...
Página 50 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
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 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
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 5 - 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.
Página 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.