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 sider |
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Side 4
... 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 no way on the length of the arms by which it is bounded . We ...
... 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 no way on the length of the arms by which it is bounded . We ...
Side 5
... Hence the radius of a circle is half the diameter . XVI . A SEMICIRCLE is the figure contained by a diameter and the part of the circumference cut off by the diameter . XVII . RECTILINEAR figures are those which are contained by ...
... Hence the radius of a circle is half the diameter . XVI . A SEMICIRCLE is the figure contained by a diameter and the part of the circumference cut off by the diameter . XVII . RECTILINEAR figures are those which are contained by ...
Side 16
... Hence every equilateral triangle is also equiangular . NOTE . When one side of a triangle is distinguished from the other sides by being called the Base , the angular point op- posite to that side is called the Vertex of the triangle ...
... Hence every equilateral triangle is also equiangular . NOTE . When one side of a triangle is distinguished from the other sides by being called the Base , the angular point op- posite to that side is called the Vertex of the triangle ...
Side 17
... Hence , by a process like that in Prop . A , we can prove the following theorem : If two angles of a triangle be equal , the sides which subtend them are also equal . ( Eucl . I. 6. ) S.E. 2 PROPOSITION C. THEOREM . If two triangles ...
... Hence , by a process like that in Prop . A , we can prove the following theorem : If two angles of a triangle be equal , the sides which subtend them are also equal . ( Eucl . I. 6. ) S.E. 2 PROPOSITION C. THEOREM . If two triangles ...
Side 18
... , L BACL BDC . Hence we see , referring to the original triangles , that L BAC - LEDF . .. , by Prop . 4 , the triangles are equal in all respects . CASE II . When the line joining the vertices does 18 [ Book L EUCLID'S ELEMENTS .
... , L BACL BDC . Hence we see , referring to the original triangles , that L BAC - LEDF . .. , by Prop . 4 , the triangles are equal in all respects . CASE II . When the line joining the vertices does 18 [ Book L EUCLID'S ELEMENTS .
Andre utgaver - Vis alle
Elements of geometry, containing books i. to vi.and portions of books xi ... Euclides,James Hamblin Smith Uten tilgangsbegrensning - 1872 |
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Ingen forhåndsvisning tilgjengelig - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 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.
Side 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...
Side 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.
Side 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.
Side 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 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.
Side 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.
Side 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.