Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1870 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 27.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 14
... similar word , and the conclusion by the word therefore . The Syllogism is exhibited in four forms , or figures , distinguished 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 , distinguished from each other by the situation of the Middle Term , or Standard of Comparison , with respect to the ...
Σελίδα 17
... .. E B and BA are at rt . angles . II . By a similar Syllogism we prove that sides D B and B C are at rt . angles , and also that sides G B and B C are at rt . angles . DEM . 3 D. 1 & 2. III . Two GEOMETRICAL REASONING . 17.
... .. E B and BA are at rt . angles . II . By a similar Syllogism we prove that sides D B and B C are at rt . angles , and also that sides G B and B C are at rt . angles . DEM . 3 D. 1 & 2. III . Two GEOMETRICAL REASONING . 17.
Σελίδα 19
... similar argument , from the commencement , proves that the square on A C is equal to the rectangle C P K. XIII . The rectangles BK and CK are together equal to the square on A B ; the squares on sides BA and AC are to- gether equal to ...
... similar argument , from the commencement , proves that the square on A C is equal to the rectangle C P K. XIII . The rectangles BK and CK are together equal to the square on A B ; the squares on sides BA and AC are to- gether equal to ...
Άλλες εκδόσεις - Προβολή όλων
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... Euclides Πλήρης προβολή - 1858 |
Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² AD² adjacent angles Algebra altitude angles equal angular points Arith Arithmetic Axioms base BC BC² bisect centre circle circumference Class-Book of Modern Concl construct defendant's book demonstration describe diagonal diameter difference distance draw a st drawn equilateral Euclid Euclid's Elements given line given point given rectilineal given st gnomon greater hypotenuse interior angles intersect isosceles triangle John Heywood join less line BC line be divided literary magnitude measure monad opposite angles opposite sides parallelogram perpendicular plaintiffs Plane Geometry premiss PROB produced Prop radius Recap rectangle rectangle contained rectilineal figure regular polygon right angles segment side AC sides equal square straight line surface truth twice Vice-Chancellor Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 175 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 95 - ... equal angles in each ; then shall the other sides be equal, each to each ; and also the third angle of the one to the third angle of the other.
Σελίδα 178 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 95 - 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.
Σελίδα 159 - 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...
Σελίδα 102 - 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...
Σελίδα 182 - 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.
Σελίδα 230 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Σελίδα 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.
Σελίδα 45 - LET it be granted that a straight line may be drawn from any one point to any other point.