Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
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Page 17
... ABCD ; we prove that A is a right angle , B a right angle , C a right angle , and D a right angle ; and we say , therefore all the angles of the figure ABCD are right angles . The argument ' a fortiori , ' by the stronger reason ...
... ABCD ; we prove that A is a right angle , B a right angle , C a right angle , and D a right angle ; and we say , therefore all the angles of the figure ABCD are right angles . The argument ' a fortiori , ' by the stronger reason ...
Page 23
... ABCD i will be divided into squares , each equal to BiPk , and thus each representing a square unit , an inch , or a foot , as the case may be in the upper row , Ahn D , there are four square units ; in the second row , hion , 4 square ...
... ABCD i will be divided into squares , each equal to BiPk , and thus each representing a square unit , an inch , or a foot , as the case may be in the upper row , Ahn D , there are four square units ; in the second row , hion , 4 square ...
Page 24
... ABCD will be equal to the squares on BC , multiplied by the linear units in AB . If BC = 4 inches , feet , & c . , and AB = 3 inches , feet , & c . , the area of ABCD will contain 4 × 3 , or 12 square inches , feet , & c . Thus the ...
... ABCD will be equal to the squares on BC , multiplied by the linear units in AB . If BC = 4 inches , feet , & c . , and AB = 3 inches , feet , & c . , the area of ABCD will contain 4 × 3 , or 12 square inches , feet , & c . Thus the ...
Page 110
... ABCD be a ☐ , and BC its diameter ; then △ A = D , and ≤ B = LC ; also △ ABC = △ BCD . BC meets the s AB and CD , and A B E Ꭰ ..the ABC = the alt . / BCD ; BC meets the || s AC and BD , .. the | ACB = the alt . ≤ CBD : Hence ...
... ABCD be a ☐ , and BC its diameter ; then △ A = D , and ≤ B = LC ; also △ ABC = △ BCD . BC meets the s AB and CD , and A B E Ꭰ ..the ABC = the alt . / BCD ; BC meets the || s AC and BD , .. the | ACB = the alt . ≤ CBD : Hence ...
Page 113
... ABCD would be in one and the same st . line . By construction BEFC is a rectangle , and the angles at C and B rt . angles ; therefore , by Prop . 14 , AB and CD will be in the same st . line with BC . F H D B E C A A E B 6. A field of ...
... ABCD would be in one and the same st . line . By construction BEFC is a rectangle , and the angles at C and B rt . angles ; therefore , by Prop . 14 , AB and CD will be in the same st . line with BC . F H D B E C A A E B 6. A field of ...
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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
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
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.