Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1870 |
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Σελίδα 63
... have their sides , which are terminated in one extremity of the base , equal to one another , and likewise those equal which are terminated in the other extremity . CONS . - Pst . 1. A st . line may be drawn from one point to another ...
... have their sides , which are terminated in one extremity of the base , equal to one another , and likewise those equal which are terminated in the other extremity . CONS . - Pst . 1. A st . line may be drawn from one point to another ...
Σελίδα 65
... have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are terminated in the other extremity . Ax . 8. Magnitudes which coincide are equal to one another . D G AN B C E F EXP ...
... have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are terminated in the other extremity . Ax . 8. Magnitudes which coincide are equal to one another . D G AN B C E F EXP ...
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
ABCD added Algebra angles equal applied Arithmetic ascertain authors Axioms base bisect centre circle circumference Class-Book common Concl construct contained defendant's demonstration describe diagonal diameter difference direction distance divided draw drawn equal Euclid extremity fall figure four Geometry given point given st greater half inch intersect join length less line BC literary magnitude means measure meet method object parallel parallelogram perpendicular plaintiffs plane Practical principles PROB Problems produced Prop proposition proved question radius reasoning Recap rectangle rectilineal representative respect right angles says scale Science segment sides similar square straight line surface taken term thing third triangle truth twice units Wherefore whole
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.