Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Part 11871 |
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... given in the Editions of August and Peyrard . To the suggestions of the late ... point , that the symbols employed in this book are admissible in the ... point as completely settled in Cambridge by the following notices prefixed to the ...
... given in the Editions of August and Peyrard . To the suggestions of the late ... point , that the symbols employed in this book are admissible in the ... point as completely settled in Cambridge by the following notices prefixed to the ...
Page 7
... point . II . That a terminated straight line may be produced to any length in a straight line . III . That a circle ... given line and whose circumference passes through the other extremity of that line . The restriction is , that the ...
... point . II . That a terminated straight line may be produced to any length in a straight line . III . That a circle ... given line and whose circumference passes through the other extremity of that line . The restriction is , that the ...
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... point st ... ...... straight rectil ....... rectilinear It is well known that one of the chief difficulties with learners of Euclid is to distinguish between what is assumed , or given ... a Problem , and what has to be proved in a Theorem ...
... point st ... ...... straight rectil ....... rectilinear It is well known that one of the chief difficulties with learners of Euclid is to distinguish between what is assumed , or given ... a Problem , and what has to be proved in a Theorem ...
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... .. BC = AB . Def . 13 . Now • AC , BC are each = AB , : . AC = BC . Ax . 1 . Thus AC , AB , BC are all equal , and an equilat . △ ABC has been described on AB . Q. E. F. PROPOSITION II . PROBLEM . From a given point to SECTION I. ...
... .. BC = AB . Def . 13 . Now • AC , BC are each = AB , : . AC = BC . Ax . 1 . Thus AC , AB , BC are all equal , and an equilat . △ ABC has been described on AB . Q. E. F. PROPOSITION II . PROBLEM . From a given point to SECTION I. ...
Page 11
Euclides James Hamblin Smith. PROPOSITION II . PROBLEM . From a given point to draw a straight line equal to a given straight line . H D B Let A be the given pt . , and BC the given st . line . It is required to draw from A a st . line ...
Euclides James Hamblin Smith. PROPOSITION II . PROBLEM . From a given point to draw a straight line equal to a given straight line . H D B Let A be the given pt . , and BC the given st . line . It is required to draw from A a st . line ...
Other editions - View all
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides No preview available - 2016 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides No preview available - 2018 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides No preview available - 2015 |
Common terms and phrases
AB=DE ABCD acute adjacent alternate angles equal angular points applied base bisected Book called centre circle coincide common construction describe diagonal difference distance divided double draw equal equidistant Euclid Exercises extremities fall figure four Geometry given point given straight line greater half Hence interior angles intersect isosceles triangle join length less Let ABC line joining magnitude measure meet method NOTE obtuse opposite sides parallel parallelogram perpendicular placed polygon position Post Postulate PROBLEM produced proof Prop PROPOSITION proved Q. E. D. Ex quadrilateral rectangle contained respects right angles Shew shewn sides square sum of sqq suppose Surface Take taken THEOREM triangle ABC triangles are equal unequal vertex vertical whole
Popular passages
Page 52 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 83 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Page 17 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 48 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Page 26 - 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, these two straight lines shall be in one and the same straight line.
Page 86 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 90 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Page 106 - 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 82 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.