Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. SmithRivingtons, 1872 - 349 sider |
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Resultat 1-5 av 90
Side 6
... produced in both directions . Euclid proceeds to put forward Six Postulates or Requests that he may be allowed to make certain assumptions on the construction of figures and the properties of geometrical mag- nitudes . Let it be granted ...
... produced in both directions . Euclid proceeds to put forward Six Postulates or Requests that he may be allowed to make certain assumptions on the construction of figures and the properties of geometrical mag- nitudes . Let it be granted ...
Side 7
... produced to any length in a straight line . III . That a circle may be described from any centre at any distance from that centre . IV . That all right angles are equal to one another . V. That two straight lines cannot inclose a space ...
... produced to any length in a straight line . III . That a circle may be described from any centre at any distance from that centre . IV . That all right angles are equal to one another . V. That two straight lines cannot inclose a space ...
Side 11
... Produce DB to meet the Oce CGH in G. With centre D and distance DG describe OGKL . Post . 3 . Produce DA to meet the Oce GKL in L. Then will AL = BC . For B is the centre of CGH , .. BC = BG . Def . 13 . And Dis the centre of OGKL ...
... Produce DB to meet the Oce CGH in G. With centre D and distance DG describe OGKL . Post . 3 . Produce DA to meet the Oce GKL in L. Then will AL = BC . For B is the centre of CGH , .. BC = BG . Def . 13 . And Dis the centre of OGKL ...
Side 14
... produced . The method of Superposition enables us also to compare magnitudes of the same kind that are unequal . For example , suppose ABC and DEF to be two given angles . LV . Suppose the arm BC to be placed on the arm EF , and the ...
... produced . The method of Superposition enables us also to compare magnitudes of the same kind that are unequal . For example , suppose ABC and DEF to be two given angles . LV . Suppose the arm BC to be placed on the arm EF , and the ...
Side 17
... produced . Again , DFE = LACB , .. FD will fall on CA ; .. D will fall on CA or CA produced . .. D must coincide with A , the only pt . common to BA and CA. .. DE will coincide with and .. is equal to AB , and DF and EDF AC , L BAC ...
... produced . Again , DFE = LACB , .. FD will fall on CA ; .. D will fall on CA or CA produced . .. D must coincide with A , the only pt . common to BA and CA. .. DE will coincide with and .. is equal to AB , and DF and EDF AC , L BAC ...
Andre utgaver - Vis alle
Elements of geometry, containing books i. to vi.and portions of books xi ... Euclides,James Hamblin Smith Uten tilgangsbegrensning - 1876 |
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
AB=DE ABCD AC=DF angle contained angles equal angular points base BC bisecting the angle centre chord circumference coincide describe diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater Hence inscribed intersect isosceles triangle LEDF less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallelogram pentagon perpendicular polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius rectangle contained Reflex Angles rhombus right angles segment shew shewn straight line joining subtended sum of sqq Take any pt tangent THEOREM touch trapezium triangle ABC triangles are equal twice rect vertex vertical angle
Populære avsnitt
Side 52 - 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 17 - 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.
Side 167 - 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.
Side 69 - 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...
Side 106 - 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 88 - If a straight line be bisected, and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected; and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D. Then the squares on AD, DB, shall be double of the squares on AC, CD.
Side 78 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 91 - 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.