Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry |
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Page 3
... common measure . Thus , 4 and 6 are commensurable , and 2 is their common measure . 6. Two quantities are said to be incommensurable , when they are not divisible by a third quantity without a remainder . Thus , 4 and 7 are not ...
... common measure . Thus , 4 and 6 are commensurable , and 2 is their common measure . 6. Two quantities are said to be incommensurable , when they are not divisible by a third quantity without a remainder . Thus , 4 and 7 are not ...
Page 4
... common denominator are 35 and 32 , and 3 is greater than 32 by 20 3 14. If the antecedents of any ratios be multiplied together , and also the consequents , a new ratio results , which is said to be compounded of the former ratios ...
... common denominator are 35 and 32 , and 3 is greater than 32 by 20 3 14. If the antecedents of any ratios be multiplied together , and also the consequents , a new ratio results , which is said to be compounded of the former ratios ...
Page 26
... common to the two triangles AFC , AGB ; therefore the base FC is equal to GB ( 4. 1. ) , and the angle ACF to ABG , and the angle AFC to AGB . Because AF is equal to AG , and the part AB to AC , the remainder BF is equal to the ...
... common to the two triangles AFC , AGB ; therefore the base FC is equal to GB ( 4. 1. ) , and the angle ACF to ABG , and the angle AFC to AGB . Because AF is equal to AG , and the part AB to AC , the remainder BF is equal to the ...
Page 28
... common to both , and the an- gle B is equal to ACB ( by the supposition ) ; therefore the triangle DBC is equal to ACB ( 4.1 . ) , the less to the greater , which is absurd . Therefore the side AB is not greater than AC . In the same ...
... common to both , and the an- gle B is equal to ACB ( by the supposition ) ; therefore the triangle DBC is equal to ACB ( 4.1 . ) , the less to the greater , which is absurd . Therefore the side AB is not greater than AC . In the same ...
Page 30
... common to the two triangles DAF , EAF , and DF is equal to EF ; the angle DAF is equal to EAF ( 8. 1. ) ; where- fore the angle BAC is bisect- ed by the straight line AF . Which was to be done . A D E F Scholium . In the same manner may ...
... common to the two triangles DAF , EAF , and DF is equal to EF ; the angle DAF is equal to EAF ( 8. 1. ) ; where- fore the angle BAC is bisect- ed by the straight line AF . Which was to be done . A D E F Scholium . In the same manner may ...
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Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair No preview available - 2023 |
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair No preview available - 2023 |
Common terms and phrases
ABC is equal ABCD alternate angles angle ABC angle ACB angle BAC angles AGH angles equal base ABC bases and altitudes bisect centre chord circumference cone Consequently cylinder demonstrations described diagonals diameter divided draw equal angles equal arches equal bases equal circles equal to AC equiangular Euclid's Euclid's Elements exterior angle fore four quantities four right angles geometry given point given straight line gles greater Hence homologous sides intersect KLMN Let ABC meet opposite angles opposite side paral parallel lines parallel to CD parallelogram parallelopipeds perp perpendicular plane polygon prism Prop pyramid Q. E. D. COR Q. E. D. PROPOSITION radius rectangle contained right angled triangle Scholium segments semicircle side AC similar similar triangles solid square straight line &c subtended tangent THEOREM triangle ABC vertex wherefore
Popular passages
Page 36 - Any two sides of a triangle are together greater than the third side.
Page 80 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 42 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Page 30 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Page 20 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 38 - Problem. At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle.
Page 113 - Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD.
Page 24 - DE ; the point B shall coincide with the point E, because AB is equal to DE; and AB coinciding with DE, AC shall coincide...
Page 36 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.