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 v
... never be found among those who go far through the propositions with no notion of distinguishing their various parts , except by differences of type or from direct labelling ; and who know they are at the end of a proposition only ...
... never be found among those who go far through the propositions with no notion of distinguishing their various parts , except by differences of type or from direct labelling ; and who know they are at the end of a proposition only ...
Σελίδα vi
... proposition , except some of the very easiest of the later ones , meets with analytical consideration before it is entered upon . By means of a series of questions and easy exercises , the pupil is led to study each part of the proposition ...
... proposition , except some of the very easiest of the later ones , meets with analytical consideration before it is entered upon . By means of a series of questions and easy exercises , the pupil is led to study each part of the proposition ...
Σελίδα 17
... Proposition III . Afterwards he may proceed , as is the usual way , to illustrate his work by freehand diagrams . 16. SOME APPLICATIONS OF THE POSTULATES . Postulate 1. - Take two points at random ; put A at one , and B at the other ...
... Proposition III . Afterwards he may proceed , as is the usual way , to illustrate his work by freehand diagrams . 16. SOME APPLICATIONS OF THE POSTULATES . Postulate 1. - Take two points at random ; put A at one , and B at the other ...
Σελίδα 22
... Proposition IV . 21. PARALLELISM . In order to complete the collection of axioms , the 12th will now be given . It ... PROPOSITIONS AND PROBLEMS 22 EUCLID BOOK I. 22.
... Proposition IV . 21. PARALLELISM . In order to complete the collection of axioms , the 12th will now be given . It ... PROPOSITIONS AND PROBLEMS 22 EUCLID BOOK I. 22.
Σελίδα 23
Euclides John Walmsley. THEOREMS AND PROBLEMS . 22. WHAT ARE PROPOSITIONS AND PROBLEMS ? Euclid's reasoning , in his " Elements , " is divided into numerous portions , generally called ' Propositions . ' Strictly speaking , a Proposition ...
Euclides John Walmsley. THEOREMS AND PROBLEMS . 22. WHAT ARE PROPOSITIONS AND PROBLEMS ? Euclid's reasoning , in his " Elements , " is divided into numerous portions , generally called ' Propositions . ' Strictly speaking , a Proposition ...
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.