An introduction to geometry, consisting of Euclid's Elements, book i, accompanied by numerous explanations, questions, and exercises, by J. Walmsley. [With] Answers, Band 11884 |
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Seite vii
... application ; and it is simply incidental that they frequently assist in the logical division of the propositions . diagrams will be found good and clear , and are repeated wherever the text requires it . The For those who are ...
... application ; and it is simply incidental that they frequently assist in the logical division of the propositions . diagrams will be found good and clear , and are repeated wherever the text requires it . The For those who are ...
Seite 4
... applies to the surface , and then looks at it from one side , trying to see between it and the surface . If he cannot see between them , the straight edge forms a straight line which lies , from one end of it to the other , wholly ' in ...
... applies to the surface , and then looks at it from one side , trying to see between it and the surface . If he cannot see between them , the straight edge forms a straight line which lies , from one end of it to the other , wholly ' in ...
Seite 16
... apply neither less nor more than he expressly demands or postu- lates . This point is dwelt upon in the questions which will now follow . C EXAMINATION XIV . 1. What is a ' postulate ' ? 2. What instrument will suffice to per- form what ...
... apply neither less nor more than he expressly demands or postu- lates . This point is dwelt upon in the questions which will now follow . C EXAMINATION XIV . 1. What is a ' postulate ' ? 2. What instrument will suffice to per- form what ...
Seite 18
... apply to all kinds of magnitude whether geome- trical or not ; and Euclid himself calls them " common notions ... applying Axioms 4 and 5 , we usually happen to know which is the greater of the pair of unequals ; and for practical ...
... apply to all kinds of magnitude whether geome- trical or not ; and Euclid himself calls them " common notions ... applying Axioms 4 and 5 , we usually happen to know which is the greater of the pair of unequals ; and for practical ...
Seite 20
... apply other modifications of the axioms , such as the following ; which are respectively related to axioms 2 , 3 , 4 , 5 , 6 , 7 : — If the same be added to equals , or if equals be added to the same , the wholes are equal . If the same ...
... apply other modifications of the axioms , such as the following ; which are respectively related to axioms 2 , 3 , 4 , 5 , 6 , 7 : — If the same be added to equals , or if equals be added to the same , the wholes are equal . If the same ...
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An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Keine Leseprobe verfügbar - 2013 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Keine Leseprobe verfügbar - 2023 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Seite 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Seite 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.
Seite 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.
Seite 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.
Seite 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Seite 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.