Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |
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Αποτελέσματα 1 - 5 από τα 33.
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 ...
... 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 ...
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 . 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 . Ax . 3 . CASE III . When AC and CD are in ...
... whole angles BAD , BDA are equal . 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 . Ax . 3 . CASE III . When AC and CD are in ...
Σελίδα 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. ] 21 PROPOSITION X.
... 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. ] 21 PROPOSITION X.
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 ; I. 34 . and BF is a diagonal of HK , .. △ HBF = ^ KFB ; I. 34 . and FD is a ...
... whole figure ABCD , and which are .. called the Complements . Then must complement AF = complement FC . • For . BD is a diagonal of AC , .. △ ABD = △ CDB ; I. 34 . and BF is a diagonal of HK , .. △ HBF = ^ KFB ; I. 34 . and FD is a ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB=DE ABCD AC=DF angles equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given line given point given straight line greater than nB Hence hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram pentagon perpendicular plane polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained reflex angle rhombus right angles segment shew shewn square subtended sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 168 - 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 7 - 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...
Σελίδα 40 - 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...
Σελίδα 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
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 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.
Σελίδα 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Σελίδα 285 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 91 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.