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 |
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Page 25
... wherefore AC and BC are each equal to AB . But things which are equal to the same thing are equal to one another ; therefore AC is equal to BC ; ( Ax . 1 ) hence AB , BC , CA are equal to one another . Therefore the triangle ABC is ...
... wherefore AC and BC are each equal to AB . But things which are equal to the same thing are equal to one another ; therefore AC is equal to BC ; ( Ax . 1 ) hence AB , BC , CA are equal to one another . Therefore the triangle ABC is ...
Page 27
... Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Q. E. F. EXERCISE V. 1. Construct the diagram for Proposition II . , similarly to the one which has been given , but making the ...
... Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Q. E. F. EXERCISE V. 1. Construct the diagram for Proposition II . , similarly to the one which has been given , but making the ...
Page 28
... wherefore the straight line AE is equal to C. ( Def . 15 ) ( Constr . ) ( Ax . 1 ) Therefore from AB , the greater of two given straight lines , a part AE has been cut off equal to the less . Q. E. F. EXAMINATION XVII . 1. Give the ...
... wherefore the straight line AE is equal to C. ( Def . 15 ) ( Constr . ) ( Ax . 1 ) Therefore from AB , the greater of two given straight lines , a part AE has been cut off equal to the less . Q. E. F. EXAMINATION XVII . 1. Give the ...
Page 32
... Wherefore , if two triangles have two sides , & c . , Which was to be demonstrated . 29. ON APPLICATIONS OF PROPOSITION IV . This proposition is put to very frequent use ; and it is required to become perfectly familiar with two sets of ...
... Wherefore , if two triangles have two sides , & c . , Which was to be demonstrated . 29. ON APPLICATIONS OF PROPOSITION IV . This proposition is put to very frequent use ; and it is required to become perfectly familiar with two sets of ...
Page 36
... Wherefore the angles A , B , C are all equal . 33. CONVERSE THEOREMS . B Q. E. D. When we compare two theorems in respect to their hypothesis and thesis , we sometimes find that the hypothesis of one is the thesis of the other ; and ...
... Wherefore the angles A , B , C are all equal . 33. CONVERSE THEOREMS . B Q. E. D. When we compare two theorems in respect to their hypothesis and thesis , we sometimes find that the hypothesis of one is the thesis of the other ; and ...
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.