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 14
... respect , are equal in respect of sides , of angles , and of area . A learner will find it useful to remember this remark when he is doing the fourth Proposition . Of four - sided figures the most important is a square , which Euclid ...
... respect , are equal in respect of sides , of angles , and of area . A learner will find it useful to remember this remark when he is doing the fourth Proposition . Of four - sided figures the most important is a square , which Euclid ...
Σελίδα 17
... respect ( see Obs . 3 on triangles , p . 13 ) . Now before he draws the con- clusion that the lines , the angles , and the areas required to be proved equal , -are equal , you will find that he will be most careful to show that the ...
... respect ( see Obs . 3 on triangles , p . 13 ) . Now before he draws the con- clusion that the lines , the angles , and the areas required to be proved equal , -are equal , you will find that he will be most careful to show that the ...
Σελίδα 42
... respect , and has to specify any particular respect in which they are equal , he begins with wherefore . ' Again , when at the close of a proposition he recapitulates what he has done , he introduces the sentence with ' wherefore ...
... respect , and has to specify any particular respect in which they are equal , he begins with wherefore . ' Again , when at the close of a proposition he recapitulates what he has done , he introduces the sentence with ' wherefore ...
Σελίδα 43
... respect , that is to say— ( 1 ) The bases , or third sides , will be equal . ( 2 ) Each pair of the remaining angles , to which the equal sides are opposite , will be equal . ( 3 ) The triangles will be equal ; that is , the quantity of ...
... respect , that is to say— ( 1 ) The bases , or third sides , will be equal . ( 2 ) Each pair of the remaining angles , to which the equal sides are opposite , will be equal . ( 3 ) The triangles will be equal ; that is , the quantity of ...
Σελίδα 53
... respect of sides , in respect of angles , and in respect of area . It will be useful to notice the three following remarks : - : - 1. In order to prove that two lines fill the same space , it is necessary to show that they begin ...
... respect of sides , in respect of angles , and in respect of area . It will be useful to notice the three following remarks : - : - 1. In order to prove that two lines fill the same space , it is necessary to show that they begin ...
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.