Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1870 |
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Σελίδα 12
... sides ; and if , of any figure placed before us , we can affirm that it has three sides exactly , the conclusion is inevitable , that this figure also is a triangle . The second kind of evidence is from the axioms , 12 GEOMETRICAL ...
... sides ; and if , of any figure placed before us , we can affirm that it has three sides exactly , the conclusion is inevitable , that this figure also is a triangle . The second kind of evidence is from the axioms , 12 GEOMETRICAL ...
Σελίδα 17
... sides about the rt . angle , together equal the square on BC , the side opposite the rt . E angle . Describe the ... sides of a square are at rt . angles to one another : EB and B A are conterminous sides of a square ; .. E B and BA are ...
... sides about the rt . angle , together equal the square on BC , the side opposite the rt . E angle . Describe the ... sides of a square are at rt . angles to one another : EB and B A are conterminous sides of a square ; .. E B and BA are ...
Σελίδα 18
... side B C is equal to the side B D ; .. the side B G is equal to the side B D. VIII . A four - sided figure of which the opposite sides are parallel , is a parallelogram : BG HA and B P K D are four - sided figures of which the opposite ...
... side B C is equal to the side B D ; .. the side B G is equal to the side B D. VIII . A four - sided figure of which the opposite sides are parallel , is a parallelogram : BG HA and B P K D are four - sided figures of which the opposite ...
Σελίδα 19
... sides BA and AC are to- gether equal to the rectangles BK and CK ; .. the squares on sides BA and AC are together equal to the square on A B. INDUCTION is a species of argument in which that is inferred respecting a whole class which ...
... sides BA and AC are to- gether equal to the rectangles BK and CK ; .. the squares on sides BA and AC are together equal to the square on A B. INDUCTION is a species of argument in which that is inferred respecting a whole class which ...
Σελίδα 27
... sides , the sum of the sides will be equal to the circumference of a circle , the radius of which equals the altitude of each triangle in the polygon ; and when that circumference is spread out into a straight line , it will represent ...
... sides , the sum of the sides will be equal to the circumference of a circle , the radius of which equals the altitude of each triangle in the polygon ; and when that circumference is spread out into a straight line , it will represent ...
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.