Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
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Side 20
... contain- ing another smaller magnitude a certain number of times , we hesitate not to say , that a line contains 10 linear units ; or a rectangle 25 square inches ; or a solid 6 cubic inches : but Plane Geometry , having to do with ...
... contain- ing another smaller magnitude a certain number of times , we hesitate not to say , that a line contains 10 linear units ; or a rectangle 25 square inches ; or a solid 6 cubic inches : but Plane Geometry , having to do with ...
Side 22
... rectangle of which the sides contain 4 and 3 linear units respectively : And generally , if we designate the number of linear units in one line by the algebraical symbol a , and the number in another line by b , the algebraical symbol ...
... rectangle of which the sides contain 4 and 3 linear units respectively : And generally , if we designate the number of linear units in one line by the algebraical symbol a , and the number in another line by b , the algebraical symbol ...
Side 23
... contained an exact number of times , as 3 times , in CD , then we say , CD is equal to 3 times AB ; thus CD = 3 AB ... Rectangle , of the Square , and of the Paral- lelogram . A e f 9 D n The sides of the rectangle , and of the square ...
... contained an exact number of times , as 3 times , in CD , then we say , CD is equal to 3 times AB ; thus CD = 3 AB ... Rectangle , of the Square , and of the Paral- lelogram . A e f 9 D n The sides of the rectangle , and of the square ...
Side 24
... contain 4 × 3 , or 12 square inches , feet , & c . Thus the product of two numbers , representing the linear units in each side of the rectangle ... containing the rectangle have an exact measuring unit . Now generalising what has been proved ...
... contain 4 × 3 , or 12 square inches , feet , & c . Thus the product of two numbers , representing the linear units in each side of the rectangle ... containing the rectangle have an exact measuring unit . Now generalising what has been proved ...
Side 129
... contained in the required figure , as existed in the given figure . Arithmetically we can say , a given triangle ... rectangle BC contains 12 square feet , —a given line , BD , or its equal EH , 2 lineal feet ; how can we apply another ...
... contained in the required figure , as existed in the given figure . Arithmetically we can say , a given triangle ... rectangle BC contains 12 square feet , —a given line , BD , or its equal EH , 2 lineal feet ; how can we apply another ...
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Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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
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Side 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...
Side 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.
Side 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.
Side 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 44 - LET it be granted that a straight line may be drawn from any one point to any other point.