The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Σελίδα 8
... radii . 18. A diameter of a circle is a right line passing through the centre , and terminated both ways by the circumference ; as , the di- ameter EF . 19. A semicircle is the figure contained by the diameter and half the circumference ...
... radii . 18. A diameter of a circle is a right line passing through the centre , and terminated both ways by the circumference ; as , the di- ameter EF . 19. A semicircle is the figure contained by the diameter and half the circumference ...
Σελίδα 11
... radii of the same circle BCD ( Def . 16. ) ; and the line BC is equal to BA , being radii of the same circle ACE : since then each of the lines AC and BC is equal to the same line AB , they are equal to one another ( Âx . 1 ...
... radii of the same circle BCD ( Def . 16. ) ; and the line BC is equal to BA , being radii of the same circle ACE : since then each of the lines AC and BC is equal to the same line AB , they are equal to one another ( Âx . 1 ...
Σελίδα 12
... radii of the same circle EGH ( Def . 16. ) , and the part DA is equal to DB , being sides of an equilateral triangle ( Const . ) , therefore the remaining part AG is equal to BE ( AX . 3. ) ; but the line BC is also equal to BE , being ...
... radii of the same circle EGH ( Def . 16. ) , and the part DA is equal to DB , being sides of an equilateral triangle ( Const . ) , therefore the remaining part AG is equal to BE ( AX . 3. ) ; but the line BC is also equal to BE , being ...
Σελίδα 18
... radii of the same circle , and EG is equal to FG ( Const . ) , and the side CG is com- mon to both ; therefore the angles CGE and CGF opposite the equal sides are equal ( Prop . 8. ) , and these are the adjacent angles ; therefore CG is ...
... radii of the same circle , and EG is equal to FG ( Const . ) , and the side CG is com- mon to both ; therefore the angles CGE and CGF opposite the equal sides are equal ( Prop . 8. ) , and these are the adjacent angles ; therefore CG is ...
Σελίδα 23
... radii of the same circle ( Def . 16. ) ; but DF is equal to B ( Const . ) , there- fore DH is equal to в ( Ax . 1. ) . Also the line EH is equal to EG , being radii of the same circle ( Def . 16. ) ; but EG is equal to c ( Const ...
... radii of the same circle ( Def . 16. ) ; but DF is equal to B ( Const . ) , there- fore DH is equal to в ( Ax . 1. ) . Also the line EH is equal to EG , being radii of the same circle ( Def . 16. ) ; but EG is equal to c ( Const ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid [Book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B and C D A B is equal ABC and ABD ABCD adjacent angles alternate angles angle ABC angle BAC angle equal angle opposite angles AGF angles CAB angles DBA base BC BC is equal BD Prop BGF and EHD bisect coincide DBC are equal demonstrated describe an equilateral diagonal draw EHD are equal equal Ax equal bases equal Hyp equal Prop equal sides equal to CD equal triangles equilateral triangle EUCLID's ELEMENTS exterior given angle given line given point greater than AC hypotenuse interior angles interior opposite angle isosceles triangle join Let the line line BC lines A B parallel Prop parallel to BC parallelogram perpendicular price One Shilling PROB produced proposition rectilineal figure respectively equal right angles Prop SCHOL side A B sides AB sides BC THEOR triangle ABC triangles are equal Twickenham vertex W. W. D. PROP
Δημοφιλή αποσπάσματα
Σελίδα 10 - Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 10 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Σελίδα 40 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 10 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 10 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 39 - 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 20 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 29 - 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 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 10 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal.