An introduction to the Elements of Euclid, being a familiar explanation of the first twelve propositions of the first book |
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Σελίδα ix
... comparing the present edition with the former , it will be found that a good deal of it has been re- written ; especially the discussion of the seventh and eighth propositions , which some , perhaps , will think too elaborate . The ...
... comparing the present edition with the former , it will be found that a good deal of it has been re- written ; especially the discussion of the seventh and eighth propositions , which some , perhaps , will think too elaborate . The ...
Σελίδα 25
... comparing these two . As soon then as you have employed the man that went by the train to serve your purpose of comparing the Lon- don and the Windsor man , cast him aside , put him out of sight , and fix your mind on the important ...
... comparing these two . As soon then as you have employed the man that went by the train to serve your purpose of comparing the Lon- don and the Windsor man , cast him aside , put him out of sight , and fix your mind on the important ...
Σελίδα 52
... compared with the foregoing to prove that the remaining angles , to which the equal sides are opposite , are equal , and that the triangles are equal . These are also proved equal by axiom 8 ; we must therefore see if they fill the same ...
... compared with the foregoing to prove that the remaining angles , to which the equal sides are opposite , are equal , and that the triangles are equal . These are also proved equal by axiom 8 ; we must therefore see if they fill the same ...
Σελίδα 58
... compared with a right appreciation of the axiom and its application . It may be true that lines , having length only , and no breadth , can fill no space ; yet if it is proved that they begin together , that they end together , and ...
... compared with a right appreciation of the axiom and its application . It may be true that lines , having length only , and no breadth , can fill no space ; yet if it is proved that they begin together , that they end together , and ...
Σελίδα 61
... triangle . In this exercise the two triangles to be compared are ABD and A CD ; and there is no doubt here which are the bases , for we are told to prove that BD is equal to DC ; and the sides to be proved EXERCISE I. ON PROP . IV . 61.
... triangle . In this exercise the two triangles to be compared are ABD and A CD ; and there is no doubt here which are the bases , for we are told to prove that BD is equal to DC ; and the sides to be proved EXERCISE I. ON PROP . IV . 61.
Συχνά εμφανιζόμενοι όροι και φράσεις
A C is equal ABC and DEF adjacent angles angle A B C angle ABC angle ACB angle B A C angle BAC angle contained angles are equal bisected centre construction D E F Definition demonstration describe an equilateral Douglas White draw a straight drawn Eighth Proposition Eleventh Proposition equal sides equal to A C equal to CL equilateral triangle Euclid exercise figure five steps follows fourth proposition given equal given point given straight line greater included angles isosceles triangle join Particular Enunciation pencil Prop PROPOSITION WRITTEN proved equal radii remaining angles required to prove respect right angles second proposition set square sides A B sides are opposite sides BA Sixth Proposition space straight line A B three straight lines triangle ABC triangles are equal vertex Wherefore write
Δημοφιλή αποσπάσματα
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 10 - 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 ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 10 - 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 103 - On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated at the other extremity equal to one another.
Σελίδα 83 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Σελίδα 123 - The neglect which he had shown of the elementary truths of geometry he afterwards regarded as a mistake in his mathematical studies ; and on a future occasion he expressed to Dr. Pemberton his regret that " he had applied himself to the works of Descartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention which so excellent a writer deserved."3 The study of Descartes...
Σελίδα 89 - AC. For, if AB be not equal to AC, one of them is greater than the other : let AB be the greater, and from it cut (i.
Σελίδα 98 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 11 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 4 - 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.