Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
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Σελίδα 25
... radius of the circle ; therefore the Area of a Circle will equal half the circumference multiplied by the radius . The diameter and circumference of a circle are incommen- surable ; but it has been ascertained that when the diameter ...
... radius of the circle ; therefore the Area of a Circle will equal half the circumference multiplied by the radius . The diameter and circumference of a circle are incommen- surable ; but it has been ascertained that when the diameter ...
Σελίδα 40
... radius . 18. A semicircle is the figure contained by the diameter and the part of the circumference cut off by the diameter ; as ADBCA . The centre of the diameter forming one boundary of the semicir le , is the same with the centre of ...
... radius . 18. A semicircle is the figure contained by the diameter and the part of the circumference cut off by the diameter ; as ADBCA . The centre of the diameter forming one boundary of the semicir le , is the same with the centre of ...
Σελίδα 44
... radius , or distance in the compasses of a given length . Euclid himself gave three other postulates , which modern Editors of the Elements place as the tenth , eleventh , and twelfth Axioms . Those postulates were - 4 . Let it be ...
... radius , or distance in the compasses of a given length . Euclid himself gave three other postulates , which modern Editors of the Elements place as the tenth , eleventh , and twelfth Axioms . Those postulates were - 4 . Let it be ...
Σελίδα 48
... radius equal to the equal sides of the triangle , and join the points A , B , and C. 3. A figure approximating to an oval may be drawn by describing , from the extremities of a given line AB , equal circles intersecting in C and F , and ...
... radius equal to the equal sides of the triangle , and join the points A , B , and C. 3. A figure approximating to an oval may be drawn by describing , from the extremities of a given line AB , equal circles intersecting in C and F , and ...
Σελίδα 49
... the line BC . The same method will be pursued in the SOLUTION : join A and C , and on AC construct an equil . triangle ADC ; produce its sides to E K H Q.E.F. C B F E and F ; and with CB as radius desc PROP . II . - BOOK I. 49.
... the line BC . The same method will be pursued in the SOLUTION : join A and C , and on AC construct an equil . triangle ADC ; produce its sides to E K H Q.E.F. C B F E and F ; and with CB as radius desc PROP . II . - BOOK I. 49.
Άλλες εκδόσεις - Προβολή όλων
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... Euclides Πλήρης προβολή - 1870 |
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 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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
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 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.
Σελίδα 44 - LET it be granted that a straight line may be drawn from any one point to any other point.