An introduction to geometry, consisting of Euclid's Elements, book i, accompanied by numerous explanations, questions, and exercises, by J. Walmsley. [With] Answers, Volume 11884 |
From inside the book
Results 1-5 of 11
Page 16
... reasoning ; and for this purpose we might use various instruments , some of which the learner will most likely have seen . Euclid , however , only requires us to know something about the use of two , namely - some instrument having a ...
... reasoning ; and for this purpose we might use various instruments , some of which the learner will most likely have seen . Euclid , however , only requires us to know something about the use of two , namely - some instrument having a ...
Page 17
... REASONING IN GEOMETRY . Numerous facts are known relating to geometrical figures ; and Euclid's object is to establish the most important of these by sound с argument . In doing so , he uses some facts THE AXIOMS . 17 AXIOMS Page 111 V ...
... REASONING IN GEOMETRY . Numerous facts are known relating to geometrical figures ; and Euclid's object is to establish the most important of these by sound с argument . In doing so , he uses some facts THE AXIOMS . 17 AXIOMS Page 111 V ...
Page 23
... reasoning , in his " Elements , " is divided into numerous portions , generally called ' Propositions . ' Strictly speaking , a Proposition is that which places before us the object of some piece of reasoning upon which we are about to ...
... reasoning , in his " Elements , " is divided into numerous portions , generally called ' Propositions . ' Strictly speaking , a Proposition is that which places before us the object of some piece of reasoning upon which we are about to ...
Page 26
... reasoning . It usually precedes the proof , but may be sometimes found partially or wholly interspersed among the steps of the reasoning . When we wish to refer to the construction as authority for some sub- sequent statement , we place ...
... reasoning . It usually precedes the proof , but may be sometimes found partially or wholly interspersed among the steps of the reasoning . When we wish to refer to the construction as authority for some sub- sequent statement , we place ...
Page 28
... reasoning of Prop . III . will be found to be so easy that we need not give any preliminary consideration to it . Its importance must not , on that account , be under - estimated , so far as Euclid's Geometry is concerned . It will be ...
... reasoning of Prop . III . will be found to be so easy that we need not give any preliminary consideration to it . Its importance must not , on that account , be under - estimated , so far as Euclid's Geometry is concerned . It will be ...
Other editions - View all
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides No preview available - 2013 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides No preview available - 2023 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides No preview available - 2018 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 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.
Page 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.
Page 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.
Page 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 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.