An introduction to geometry, consisting of Euclid's Elements, book i, accompanied by numerous explanations, questions, and exercises, by J. Walmsley. [With] Answers, Τόμος 11884 |
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Σελίδα vi
... proof will be founded , full proofs being afterwards taken orally with the blackboard . Proceeding in this way , it is evident that in regard to much of the practical work of the class the teacher may correct , with or without the aid ...
... proof will be founded , full proofs being afterwards taken orally with the blackboard . Proceeding in this way , it is evident that in regard to much of the practical work of the class the teacher may correct , with or without the aid ...
Σελίδα vii
... proofs in some cases , a series of alternative ones is given in an Appendix , consisting of those which are likely to find most . favour with teachers . They are expressed with the aid of symbols , in order to assist , at the same time ...
... proofs in some cases , a series of alternative ones is given in an Appendix , consisting of those which are likely to find most . favour with teachers . They are expressed with the aid of symbols , in order to assist , at the same time ...
Σελίδα 14
... proofs . A trapezium having two sides parallel is called a ' trapezoid . ' The word trapezium itself is sometimes used with this meaning . Obs . - The next three Examinations are intended to be taken in con- junction with a revision of ...
... proofs . A trapezium having two sides parallel is called a ' trapezoid . ' The word trapezium itself is sometimes used with this meaning . Obs . - The next three Examinations are intended to be taken in con- junction with a revision of ...
Σελίδα 18
... proof are usually called axioms . It is clearly necessary that they should be chosen with special care and skill . Euclid performs this service for us in Geometry ; and in selecting his axioms he appears to adopt as his rule that each ...
... proof are usually called axioms . It is clearly necessary that they should be chosen with special care and skill . Euclid performs this service for us in Geometry ; and in selecting his axioms he appears to adopt as his rule that each ...
Σελίδα 19
... Proof . It is given that DH is equal to AB ; H B and because A is the centre of the circle BCD , therefore AC is also equal to AB . ( Def . 15 ) But things which are equal to the same thing are equal to one another . Therefore DH and AC ...
... Proof . It is given that DH is equal to AB ; H B and because A is the centre of the circle BCD , therefore AC is also equal to AB . ( Def . 15 ) But things which are equal to the same thing are equal to one another . Therefore DH and AC ...
Άλλες εκδόσεις - Προβολή όλων
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC is equal adjacent angles alternate angle angle ABC angle ACB angle AGH angle BAC angle BCD angle equal angles CBA axiom base BC bisects the angle centre circle circumference Constr construction definition describe diagonal Diagram diameter enunciation equal and parallel equal angles equal sides equal to BC EQUIANGULAR POLYGONS equilateral triangle Euclid Euclid's Elements exterior four right angles Geometry given angle given point given straight line greater hypotenuse hypothesis inference isosceles triangle join less Let ABC magnitude meet middle point opposite angles opposite interior angle opposite sides pair of equal parallel to BC parallelogram perpendicular Postulate produced proof Prop proposition prove quadrilateral rectilineal figure respectively equal rhombus right angles right-angled triangle sides equal square supplementary angles theorems thesis trapezium triangle ABC triangles are equal unequal vertex Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 132 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 86 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 139 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Σελίδα 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Σελίδα 134 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 50 - if two straight lines" &c. QED COR. 1. From this it is manifest, that if two straight lines cut one another, the angles which they make at the point where they cut, are together equal to four right angles.
Σελίδα 20 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Σελίδα 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 49 - If at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight line.