Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
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Page iii
... similar Schools , who have not much time for the pursuit of Geometrical Studies , and to whom , therefore , the Practical Applica- tion of whatever they learn is of great importance . He is , however , persuaded that those who have both ...
... similar Schools , who have not much time for the pursuit of Geometrical Studies , and to whom , therefore , the Practical Applica- tion of whatever they learn is of great importance . He is , however , persuaded that those who have both ...
Page vi
... similar work , -the Definitions , Postulates , and Axioms of which the leading words are printed ; and thirdly , that he should proceed to take the Propositions in order , and write out the proofs at large , as the printed forms and ...
... similar work , -the Definitions , Postulates , and Axioms of which the leading words are printed ; and thirdly , that he should proceed to take the Propositions in order , and write out the proofs at large , as the printed forms and ...
Page viii
... similar Schools , —the objects of the Editor will be accomplished . He desires no worthier calling than to be a fellow- labourer with the many excellent and talented Masters to whom , in the National , British , and other Public Schools ...
... similar Schools , —the objects of the Editor will be accomplished . He desires no worthier calling than to be a fellow- labourer with the many excellent and talented Masters to whom , in the National , British , and other Public Schools ...
Page 3
... similar figures , and of Proportion as applied to Geometry . Our proposed limits confine us , for the present at least , to the first and second books . The first book , besides the Definitions , Postulates , and Axioms , contains forty ...
... similar figures , and of Proportion as applied to Geometry . Our proposed limits confine us , for the present at least , to the first and second books . The first book , besides the Definitions , Postulates , and Axioms , contains forty ...
Page 13
... similar word , and the conclusion by the word therefore . The Syllogism is exhibited in four forms , or figures , distin- guished from each other by the situation of the Middle Term , or Standard of Comparison , with respect to the ...
... similar word , and the conclusion by the word therefore . The Syllogism is exhibited in four forms , or figures , distin- guished from each other by the situation of the Middle Term , or Standard of Comparison , with respect to the ...
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Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles Algebra altitude angle equal angular point Arith Arithmetic ascertain Axiom bisect centre circle circumference Concl CONS construct DEANSGATE DEMONSTRATION.-P describe diagonal diameter distance drawn equal bases equilateral Euclid Euclid's Elements extremity Geometry given line given point given rectilineal given st greater hypotenuse inch interior angles intersect isosceles triangle JOHN HEYWOOD join LADC length less line be divided lines AC magnitude measure monad opposite angles opposite sides parallel parallelogram perpendicular plane Plane Geometry polygon premiss PROB produced Prop proposition Quæs radius Recap rectangle rectangle contained rectilineal angle rectilineal figure regular polygon right angles SCHOLIUM.-1 segment sides equal straight line surface trapezium twice vertical angle Wherefore
Popular passages
Page 93 - 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. either the sides adjacent to the equal...
Page 105 - 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 161 - 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 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Page 93 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 100 - 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 180 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 18 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 142 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Page 44 - LET it be granted that a straight line may be drawn from any one point to any other point.