Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1870 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 90.
Σελίδα 10
... angle equal to a right angle , or to 90 ° . The Supplement of an angle ( supplementum , a filling up ) is what is wanted to make an angle equal to two right angles , or to 180 ° . The Explement of an angle ( explementum , a filling ) is ...
... angle equal to a right angle , or to 90 ° . The Supplement of an angle ( supplementum , a filling up ) is what is wanted to make an angle equal to two right angles , or to 180 ° . The Explement of an angle ( explementum , a filling ) is ...
Σελίδα 11
... angle we fill up the unoccupied space between the other two : it will thus appear that the three angles which we cut off from the original triangle are together equal ... equal ; and the demonstration shows by strict argument or reasoning ...
... angle we fill up the unoccupied space between the other two : it will thus appear that the three angles which we cut off from the original triangle are together equal ... equal ; and the demonstration shows by strict argument or reasoning ...
Σελίδα 15
... equal to the line A C , Minor P. and Z = Y ; and the line BC is equal to the line AB ; therefore , the line BC is ... angle D B C is a right angle , Minor P. and Z = Y ; and the angle F B A is a right angle ; therefore , the angle FB A ...
... equal to the line A C , Minor P. and Z = Y ; and the line BC is equal to the line AB ; therefore , the line BC is ... angle D B C is a right angle , Minor P. and Z = Y ; and the angle F B A is a right angle ; therefore , the angle FB A ...
Σελίδα 16
... angle , or Y , the predicate of the minor premiss ; DBC , or X , is the subject , and rt . angle , or Y , the ... equal to Minor P. and Y = Z ; and < EG B is equal to AGH ; therefore , A G H is equal to GHD . Concl . therefore , Z = X ...
... angle , or Y , the predicate of the minor premiss ; DBC , or X , is the subject , and rt . angle , or Y , the ... equal to Minor P. and Y = Z ; and < EG B is equal to AGH ; therefore , A G H is equal to GHD . Concl . therefore , Z = X ...
Σελίδα 18
... angle EBG is equal to the angle ABC . IV . All the sides of a square are equal : A B and B E are sides of a square ; FA H E B P D K .. A B and B E are equal sides . v . All right angles are equal : BEG and BAC are rt . angles ; .. △ BE ...
... angle EBG is equal to the angle ABC . IV . All the sides of a square are equal : A B and B E are sides of a square ; FA H E B P D K .. A B and B E are equal sides . v . All right angles are equal : BEG and BAC are rt . angles ; .. △ BE ...
Άλλες εκδόσεις - Προβολή όλων
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... Euclides Πλήρης προβολή - 1858 |
Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² AD² adjacent angles Algebra altitude angles equal angular points Arith Arithmetic Axioms base BC BC² bisect centre circle circumference Class-Book of Modern Concl construct defendant's book demonstration describe diagonal diameter difference distance draw a st drawn equilateral Euclid Euclid's Elements given line given point given rectilineal given st gnomon greater hypotenuse interior angles intersect isosceles triangle John Heywood join less line BC line be divided literary magnitude measure monad opposite angles opposite sides parallelogram perpendicular plaintiffs Plane Geometry premiss PROB produced Prop radius Recap rectangle rectangle contained rectilineal figure regular polygon right angles segment side AC sides equal square straight line surface truth twice Vice-Chancellor Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 175 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 95 - ... equal angles in each ; then shall the other sides be equal, each to each ; and also the third angle of the one to the third angle of the other.
Σελίδα 178 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 95 - 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 159 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Σελίδα 102 - 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 182 - 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 230 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
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 45 - LET it be granted that a straight line may be drawn from any one point to any other point.