Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
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Σελίδα v
... Problems contained in the Elements of Plane Geometry . He will not , indeed , have arrived at the means of demonstrating the prob- lems , which lie out of the First and Second Books ; but , inasmuch as their construction depends almost ...
... Problems contained in the Elements of Plane Geometry . He will not , indeed , have arrived at the means of demonstrating the prob- lems , which lie out of the First and Second Books ; but , inasmuch as their construction depends almost ...
Σελίδα 3
... problems for giving power to construct various lines , angles , and figures ; and thirty - four are theorems , being the expositions of new geometrical truths . Of these theo- reins , some may be regarded as simply subsidiary to the ...
... problems for giving power to construct various lines , angles , and figures ; and thirty - four are theorems , being the expositions of new geometrical truths . Of these theo- reins , some may be regarded as simply subsidiary to the ...
Σελίδα 4
... problems , the other twelve are theorems . Props . 12 and 13 give the Elements of Trigonometrical Analysis , or the Arithmetic of sines , and are of great use in the Higher Geometry : the other propositions may be classified according ...
... problems , the other twelve are theorems . Props . 12 and 13 give the Elements of Trigonometrical Analysis , or the Arithmetic of sines , and are of great use in the Higher Geometry : the other propositions may be classified according ...
Σελίδα 5
... a point between them , as AB.CD , de- note , not the product of A B multiplied by CD , but the rectangle formed by two of its sides meeting in a common point . III . - Abbreviations . Prob . .... Problem . SYMBOLICAL NOTATION . 5.
... a point between them , as AB.CD , de- note , not the product of A B multiplied by CD , but the rectangle formed by two of its sides meeting in a common point . III . - Abbreviations . Prob . .... Problem . SYMBOLICAL NOTATION . 5.
Σελίδα 6
Euclides Henry Green. III . - Abbreviations . Prob . .... Problem . Add ..... Addendo , by adding . Ax . Conc . Cor . ..Axiom . .Conclusion , inference . .Corollary . Cons . .... Construction . C. 1 & c . .. Step 1 & c . of the Con- Dat ...
Euclides Henry Green. III . - Abbreviations . Prob . .... Problem . Add ..... Addendo , by adding . Ax . Conc . Cor . ..Axiom . .Conclusion , inference . .Corollary . Cons . .... Construction . C. 1 & c . .. Step 1 & c . of the Con- Dat ...
Άλλες εκδόσεις - Προβολή όλων
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... Euclides Πλήρης προβολή - 1870 |
Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD added Algebra angle equal angular applied Arithmetic ascertain Axiom base bisect called centre circle circumference common Concl CONS construct contained demonstration describe diagonal diameter difference distance divided double draw drawn Euclid extremity fall feet figure four Geometry give given line given point greater half inch intersect join length less line BC magnitude MAPS means measure meet method miles object opposite sides parallel parallelogram perpendicular plane Practical principle PROB problem produced Prop proposition proved radius Recap rectangle representative respect right angles scale segment sides similar square straight line surface taken term thing third triangle truth twice units Wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 44 - LET it be granted that a straight line may be drawn from any one point to any other point.