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 σελίδες |
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Σελίδα 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 no ...
... 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 no ...
Σελίδα 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 ...
Σελίδα 19
... whole angles BAD , BDA are equal , = 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 are ...
... whole angles BAD , BDA are equal , = 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 are ...
Σελίδα 21
... Produce a given 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. PROP . X. 21.
... Produce a given 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. PROP . X. 21.
Σελίδα 69
... whole figure ABCD , and which are .. called the Complements . Then must complement AF - complement FC . For BD is a diagonal of □ AC , .ABD : = △ CDB ; and BF is a diagonal of ☐ HK , : . A HBF & KFB ; and FD is a diagonal of EG ...
... whole figure ABCD , and which are .. called the Complements . Then must complement AF - complement FC . For BD is a diagonal of □ AC , .ABD : = △ CDB ; and BF is a diagonal of ☐ HK , : . A HBF & KFB ; and FD is a diagonal of EG ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC=DF angles equal angular points base BC bisecting the angle centre chord circumference coincide diagonals diameter divided equal angles equal circles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given line given point given st given straight line greater Hence hypotenuse inscribed isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained Reflex Angles required to describe rhombus right angles segment semicircle shew shewn straight line joining subtended sum of sqq Take any pt tangent THEOREM trapezium triangle ABC triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.