Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
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Page 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 is ...
... 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 is ...
Page 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 ...
Page 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 granted ...
... 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 granted ...
Page 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 A B , equal circles intersecting in C and F ...
... 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 A B , equal circles intersecting in C and F ...
Page 49
... line BC . The same method will be pursued in the E SOLUTION : join A and C , and on AC construct an equil . triangle ADC ; produce its sides to E K H C Q.E.F. B E and F ; and with CB as radius desc PROP . II . - BOOK I. 49.
... line BC . The same method will be pursued in the E SOLUTION : join A and C , and on AC construct an equil . triangle ADC ; produce its sides to E K H C Q.E.F. B E and F ; and with CB as radius desc PROP . II . - BOOK I. 49.
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Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides No preview available - 2016 |
Common terms and phrases
ABCD added Algebra angle equal angular applied Arithmetic ascertain Axiom base bisect called centre circle circumference common Concl CONS construct contained demonstration describe diagonal diameter difference distance divided double draw drawn Euclid extremity fall feet figure four Geometry give given line given point greater half inch intersect join length less line BC magnitude MAPS means measure meet method miles object opposite sides parallel parallelogram perpendicular plane Practical principle PROB problem produced Prop proposition proved radius Recap rectangle representative respect right angles scale segment sides similar square straight line surface taken term thing third triangle truth twice units Wherefore whole
Popular passages
Page 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...
Page 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.
Page 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.
Page 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Page 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.
Page 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...
Page 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.
Page 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.
Page 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.
Page 44 - LET it be granted that a straight line may be drawn from any one point to any other point.