The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Del 1John Weale, 1853 - 136 sider |
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Side xix
... EFGH ) are upon equal bases and between the same parallels , CONSEQUENCE . - They are equal to one another in area . CONSTRUCTION . - Draw BE and CH . XX INTRODUCTION . DEMONSTRATION . Syllogism 1 . Da ( INTRODUCTION . xix.
... EFGH ) are upon equal bases and between the same parallels , CONSEQUENCE . - They are equal to one another in area . CONSTRUCTION . - Draw BE and CH . XX INTRODUCTION . DEMONSTRATION . Syllogism 1 . Da ( INTRODUCTION . xix.
Side xx
... base and between the same parallels ) ARE equal in area . [ I. 35. ] ri ABCD and EBCH ARE ( parallelograms which are upon the same base and between the same parallels . ) [ Hypoth . and syl . 2. ] JX alk i Therefore ABCD and EBCH ARE ...
... base and between the same parallels ) ARE equal in area . [ I. 35. ] ri ABCD and EBCH ARE ( parallelograms which are upon the same base and between the same parallels . ) [ Hypoth . and syl . 2. ] JX alk i Therefore ABCD and EBCH ARE ...
Side 4
... base of the triangle , the other two lines being termed its sides , and the point in which the two sides meet is termed the vertex . 20. An EQUILATERAL TRIANGLE is a triangle which has three sides equal . 21. An ISOSCELES TRIANGLE is a ...
... base of the triangle , the other two lines being termed its sides , and the point in which the two sides meet is termed the vertex . 20. An EQUILATERAL TRIANGLE is a triangle which has three sides equal . 21. An ISOSCELES TRIANGLE is a ...
Side 11
... bases or third sides ( EF and BC ) will be equal ; [ 2 ] and the angles at the bases , which are opposite to the equal ... base EF , and be equal to it ( c ) ; for otherwise two straight lines would enclose a space ( a ) . [ 2. ] And as ...
... bases or third sides ( EF and BC ) will be equal ; [ 2 ] and the angles at the bases , which are opposite to the equal ... base EF , and be equal to it ( c ) ; for otherwise two straight lines would enclose a space ( a ) . [ 2. ] And as ...
Side 12
... base ( ABC and ACB ) are equal to one another ; [ 2 ] and if the equal sides be produced , the angles formed by the produced sides and the base below the same ( CBD and BCE ) shall be equal . CONSTRUCTION . Produce the equal sides AB ...
... base ( ABC and ACB ) are equal to one another ; [ 2 ] and if the equal sides be produced , the angles formed by the produced sides and the base below the same ( CBD and BCE ) shall be equal . CONSTRUCTION . Produce the equal sides AB ...
Andre utgaver - Vis alle
The elements of Euclid, [books I.-VI. XI. XII.] with many additional ... Eucleides Uten tilgangsbegrensning - 1853 |
The Elements of Euclid with Many Additional Propositions and Explanatory Notes Henry Law,Eucleides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
AC and CB AC is equal angle ABC angle BCD angle equal area to double area to twice bisect chord circle ABC circumference Constr CONSTRUCTION COROLLARY DB is equal DEMONSTRATION diagonal divided double the rectangle draw equal angles equal in area equal to AC equilateral Euclid external angle Find the center finite straight line Geometry given angle given line greater Hypoth HYPOTHESES intersect join less line BC lines be drawn magnitude major premiss opposite sides parallel parallelogram perpendicular predicate premises produced proposition quadratic equation reductio ad absurdum right angles SCHOLIA SCHOLIUM second power segment sides AC square on AC square on half squares on AB syllogism termed THEOREM THEOREM.-If triangle ABC twice the rectangle twice the square vertex whole line
Populære avsnitt
Side 24 - 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.
Side 114 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Side xiv - 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 : 16. And this point is called the centre of the circle.
Side 13 - The difference between any two sides of a triangle is less than the third side.
Side 111 - AFC. (in. 21.) Hence in the triangles ADE, AFC, there are two angles in the one respectively equal to two angles in the other, consequently, the third angle CAF is equal to the third angle DAB ; therefore the arc DB is equal to the arc CF, (in.
Side 89 - ... the centre of the circle shall be in that line. Let the straight line DE touch the circle ABC in C, and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA.
Side 70 - EQUAL circles are those of which the diameters are equal, or from the centres of which the straight lines to the circumferences are equal. ' This is not a definition, but a theorem, the truth of ' which is evident; for, if the circles be applied to one ' another, so that their centres coincide, the circles ' must likewise coincide, since the straight lines from
Side 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Side 22 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...