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 17
... equal to one another . Modern geometricians have tried to remove this eleventh axiom from the list of axioms , and to give a proof that all right angles are equal ; hereafter you may examine such proofs . The twelfth axiom is not ...
... equal to one another . Modern geometricians have tried to remove this eleventh axiom from the list of axioms , and to give a proof that all right angles are equal ; hereafter you may examine such proofs . The twelfth axiom is not ...
Σελίδα 18
... given ; in the fifth proposition a triangle having two equal sides is given . In some of the propositions , starting from the given foundation ( or , as it is commonly called , hypothesis , ' from vо - Ti0n , to lay down as a foundation ) ...
... given ; in the fifth proposition a triangle having two equal sides is given . In some of the propositions , starting from the given foundation ( or , as it is commonly called , hypothesis , ' from vо - Ti0n , to lay down as a foundation ) ...
Σελίδα 26
... Given a finite straight line : -- It is required to describe an equilateral triangle upon it . Particular ... equal to A B , because they are radii of the same circle B C D ( Def . 15 ) . 2. C B is equal to A B , because they are radii ...
... Given a finite straight line : -- It is required to describe an equilateral triangle upon it . Particular ... equal to A B , because they are radii of the same circle B C D ( Def . 15 ) . 2. C B is equal to A B , because they are radii ...
Σελίδα 27
... equal to one another . Therefore A C is equal to CB ( Ax . 1 ) . 5. Wherefore C A , A B , and BC are all equal to one another , and the triangle ABC is therefore equi- lateral , and it is described on the given straight line A B , which ...
... equal to one another . Therefore A C is equal to CB ( Ax . 1 ) . 5. Wherefore C A , A B , and BC are all equal to one another , and the triangle ABC is therefore equi- lateral , and it is described on the given straight line A B , which ...
Σελίδα 28
... given , and what has to be done in the Second Proposition , is thus answered in the General Enunciation . Given a point , and a straight line : - It is required from the given point to draw a straight line equal to the given straight ...
... given , and what has to be done in the Second Proposition , is thus answered in the General Enunciation . Given a point , and a straight line : - It is required from the given point to draw a straight line equal to the given straight ...
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.