An introduction to the Elements of Euclid, being a familiar explanation of the first twelve propositions of the first book |
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Αποτελέσματα 1 - 5 από τα 83.
Σελίδα 9
... angles CDA and CDB [ these are called adjacent angles ] are equal , each of the two is a right angle . D B If you hold the ruler so as to make one of the adjacent angles greater than the other , then the greater angle , C D A , is ...
... angles CDA and CDB [ these are called adjacent angles ] are equal , each of the two is a right angle . D B If you hold the ruler so as to make one of the adjacent angles greater than the other , then the greater angle , C D A , is ...
Σελίδα 10
... 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 perpen- dicular to it . Definition 11. - An obtuse angle is that which is greater than a right angle ...
... 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 perpen- dicular to it . Definition 11. - An obtuse angle is that which is greater than a right angle ...
Σελίδα 12
... sides . are equal , the triangle is equilateral ( from æquus , equal ; latus , side ) . Definition 25. - If two sides only are equal , the triangle is isosceles ( from ioos , equal ; okéλos , leg ) . Definition 26. - If all the three ...
... sides . are equal , the triangle is equilateral ( from æquus , equal ; latus , side ) . Definition 25. - If two sides only are equal , the triangle is isosceles ( from ioos , equal ; okéλos , leg ) . Definition 26. - If all the three ...
Σελίδα 14
... sides are equal each to each : -that the three angles are equal each to each : -- and that the enclosed surfaces or areas are equal . In fact , two triangles equal in every respect , are equal in respect of sides , of angles , and of ...
... sides are equal each to each : -that the three angles are equal each to each : -- and that the enclosed surfaces or areas are equal . In fact , two triangles equal in every respect , are equal in respect of sides , of angles , and of ...
Σελίδα 17
... angles are 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 ...
... angles are 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 ...
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.