Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryW. E. Dean, 1842 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 50.
Σελίδα 4
... definition , except that of EUCLID , has ever been given , from which the properties of proportionals can be deduced ... definitions in the first Book , and particularly on that of a straight line . A new axiom is also introduced in the ...
... definition , except that of EUCLID , has ever been given , from which the properties of proportionals can be deduced ... definitions in the first Book , and particularly on that of a straight line . A new axiom is also introduced in the ...
Σελίδα 5
... Definitions , Propositions , Axioms , Theorems , Problems , Lemmas , Scho- liums , Corollaries , & c . 3. A Definition ... definition ought to be clear , and expressed in words that are common and perfectly well understood . 4. An Axiom ...
... Definitions , Propositions , Axioms , Theorems , Problems , Lemmas , Scho- liums , Corollaries , & c . 3. A Definition ... definition ought to be clear , and expressed in words that are common and perfectly well understood . 4. An Axiom ...
Σελίδα 7
... first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post . ) the second postulate ; ( Def . 3. ) the third definition , and so on . 29. The word , therefore , or hence , frequently OF GEOMETRY . BOOK I.
... first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post . ) the second postulate ; ( Def . 3. ) the third definition , and so on . 29. The word , therefore , or hence , frequently OF GEOMETRY . BOOK I.
Σελίδα 8
... DEFINITIONS . 1. " A POINT is that which has position , but not magnitude * . " ( See Notes . ) 2. A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the intersections " of one line with another ...
... DEFINITIONS . 1. " A POINT is that which has position , but not magnitude * . " ( See Notes . ) 2. A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the intersections " of one line with another ...
Σελίδα 12
... Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
... Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 149 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of...
Σελίδα 12 - 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.
Σελίδα 9 - 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 52 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 80 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 296 - 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 50 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 15 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...