Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1870 |
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Σελίδα 1
... measure- ments were made , while as yet there was no accurate theory of measuring - no abstract speculations concerning space and its properties . The points and lines of such a Geometry were necessarily visible quantities . A mark ...
... measure- ments were made , while as yet there was no accurate theory of measuring - no abstract speculations concerning space and its properties . The points and lines of such a Geometry were necessarily visible quantities . A mark ...
Σελίδα 22
... measuring , became a theoretical Science , have in their very elements the property of extension ; they do , and they must , occupy space . On the Atomic theory of Chemistry , there are ultimate atoms beyond which no actual division of ...
... measuring , became a theoretical Science , have in their very elements the property of extension ; they do , and they must , occupy space . On the Atomic theory of Chemistry , there are ultimate atoms beyond which no actual division of ...
Σελίδα 23
... measures a surface in its length is made up of the units or monads of length ; and the line which measures the same surface in its breadth is made up of the same units or monads , in this case called breadth . The monad of length and ...
... measures a surface in its length is made up of the units or monads of length ; and the line which measures the same surface in its breadth is made up of the same units or monads , in this case called breadth . The monad of length and ...
Σελίδα 24
... measure- ment of length and the measurement of breadth , and the combination of the two as indicating the measurement of surface . Lines and Surfaces , as well as all other magnitudes , may be expressed by numbers ; indeed , without ...
... measure- ment of length and the measurement of breadth , and the combination of the two as indicating the measurement of surface . Lines and Surfaces , as well as all other magnitudes , may be expressed by numbers ; indeed , without ...
Σελίδα 25
... measuring line for CD : we now seek for a third line , as E ; and if this third line is contained an exact number of times , as twice , in AB , and an exact number of times , as seven times , in CD , then E is the common measuring line ...
... measuring line for CD : we now seek for a third line , as E ; and if this third line is contained an exact number of times , as twice , in AB , and an exact number of times , as seven times , in CD , then E is the common measuring line ...
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.