Outlines of Geometry ... |
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Σελίδα 33
... expressed in an algebraic form , thus : - · -- If n be the number of sides of any polygon , then the sum of its angles 2 ( n - 2 ) - = ( n − 2 ) 180 ° . And therefore , if the polygon be regular , the П 2 - number of degrees in any one ...
... expressed in an algebraic form , thus : - · -- If n be the number of sides of any polygon , then the sum of its angles 2 ( n - 2 ) - = ( n − 2 ) 180 ° . And therefore , if the polygon be regular , the П 2 - number of degrees in any one ...
Σελίδα 69
... expressed in an easier and more general manner , it is hopeless to attempt to analyse more difficult loci . For a ... expression of their properties so simple that in any given locus they can 69.
... expressed in an easier and more general manner , it is hopeless to attempt to analyse more difficult loci . For a ... expression of their properties so simple that in any given locus they can 69.
Σελίδα 71
... expressed in terms of the length of the other . " In a similar manner , in the above case the length of one co - ordinate may be expressed in terms of the other , and if these two quantities be represented by the two variables , x and y ...
... expressed in terms of the length of the other . " In a similar manner , in the above case the length of one co - ordinate may be expressed in terms of the other , and if these two quantities be represented by the two variables , x and y ...
Σελίδα 78
... expressed exponentially it will be found that ( ) becomes a biquadratic equation , in terms of e which if p be a root , s = ( − ) c log . p - ds = ( - ) c2 ~ ) c2dp2 p2 But dx dy = ds ' ··· p2dx2 + p2dy ' + c2dp2 = 0 ( 1 ) ( k ) ( a ) ...
... expressed exponentially it will be found that ( ) becomes a biquadratic equation , in terms of e which if p be a root , s = ( − ) c log . p - ds = ( - ) c2 ~ ) c2dp2 p2 But dx dy = ds ' ··· p2dx2 + p2dy ' + c2dp2 = 0 ( 1 ) ( k ) ( a ) ...
Σελίδα 84
... expressed by means of an equation . If , then , the equation which expresses this relation be given for any particular curve - say for an ellipse , we are enabled , by introducing the modifications due to the fact that PQ , PR , RQ are ...
... expressed by means of an equation . If , then , the equation which expresses this relation be given for any particular curve - say for an ellipse , we are enabled , by introducing the modifications due to the fact that PQ , PR , RQ are ...
Άλλες εκδόσεις - Προβολή όλων
Outlines of Geometry: Or, the Motion of a Point Walter Marsham Adams Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Outlines of Geometry; Or, the Motion of a Point Walter Marsham Adams Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
Algebra Algebraic Geometry already arrest ascertained axis becomes boundary points breadth burning-glass calculated called centre CHAPTER circumference conceived Conic Sections considered course curve Cycloid Cyclone cyclonoid decrease deduced definite distance depends Descartes described determine Differential Calculus directions with regard ellipse enclosed equation Euclid examine example Existence figure fixed point force of impulsion further geometrical given point gradually increase Hence Hyperbola idea infinite Infinitesimal Calculus infinity latter law of motion length Loci locus magnitude Mathematics means measure method moving point namely number of degrees number of straight object observed obtained opposite orbit Parabola pass plane point in common point move polygon principle PROBLEM OF PYTHAGORAS proved radius Rectangular Co-ordinates relation right angles space storm field straight line drawn subtends Suppose surface tangent theodolite three consecutive points three points tion treatise triangle Trigonometry vary wind words zero
Δημοφιλή αποσπάσματα
Σελίδα 52 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 23 - 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 26 - A segment of a circle is the figure contained by a straight line and the circumference it cuts off.
Σελίδα 29 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 21 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Σελίδα 51 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Σελίδα 51 - Let BAC be the given rectilineal angle, it is required to bisect it. Take any point D in AB, and from AC cut (i.
Σελίδα 41 - all right angles (for example) are equal to one another ; " that " when one straight line falling on two other straight lines makes the two interior angles on the same side less than two right angles, these two straight lines, if produced, shall meet on the side, where are the two angles less than two right angles ; " are manifestly principles which bear no analogy to such barren truisms as these, " Things that are equal to one and the same thing are equal to one another.
Σελίδα 80 - ... but the wind drew round and round, according to the now known laws of these circular storms, and she, with a perseverance that might have been more wisely employed, continued to scud " right before it " for four successive days and nights, by which time she had actually circumnavigated the storm-field five times.
Σελίδα 22 - And that a circle may be described from any centre, at any distance from that centre.