The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 1
... A point is that which has no parts , or which has no magnitude . A line is length without breadth . II . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . V. A ...
... A point is that which has no parts , or which has no magnitude . A line is length without breadth . II . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . V. A ...
Σελίδα 2
... a point , it may be expressed by a letter placed at that point , as the angle at E. " X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ...
... a point , it may be expressed by a letter placed at that point , as the angle at E. " X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ...
Σελίδα 7
... given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral ... point C , in which the circles cut one another , draw ( Post . 1. ) the straight lines CA , CB , to the points 4 , B ; ABC shall ...
... given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral ... point C , in which the circles cut one another , draw ( Post . 1. ) the straight lines CA , CB , to the points 4 , B ; ABC shall ...
Σελίδα 8
... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
Σελίδα 13
... a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point Din AB , and from AC cut ( I. 3. ) off AE equal to AD ; join DE , and upon ...
... a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point Din AB , and from AC cut ( I. 3. ) off AE equal to AD ; join DE , and upon ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle