Introductory Modern Geometry of Point, Ray, and Circle |
From inside the book
Results 1-5 of 22
Page 23
... given tract , or that on any ray we could find two points , A and B , as far apart as two other points , A ' and B ' . This assumption that something can be done , is called a Postulate ( airnμa ) , i.e. a demand , which must be granted ...
... given tract , or that on any ray we could find two points , A and B , as far apart as two other points , A ' and B ' . This assumption that something can be done , is called a Postulate ( airnμa ) , i.e. a demand , which must be granted ...
Page 29
... given in extenso is a specimen of a syllogism ( σvoyoμos = computation = thinking together ) . The first two propositions are called premisses , the third and last , in which the other two are thought together , is called conclusion ...
... given in extenso is a specimen of a syllogism ( σvoyoμos = computation = thinking together ) . The first two propositions are called premisses , the third and last , in which the other two are thought together , is called conclusion ...
Page 44
... DPD ' be isosceles , then the normal PN is the medial of the base ( why ? ) . F. Two , and only two , tracts of given length can be drawn from a point to a ray . Proof . For two , and only two , points 44 [ TH . XXIII . GEOMETRY .
... DPD ' be isosceles , then the normal PN is the medial of the base ( why ? ) . F. Two , and only two , tracts of given length can be drawn from a point to a ray . Proof . For two , and only two , points 44 [ TH . XXIII . GEOMETRY .
Page 45
... given distance from the foot of the normal . G. Of tracts drawn to points unequally distant from the foot of the normal , the one drawn to the remotest is the longest . Proof . In the △ PDA , angle PDA > PAD ( why ? ) ; hence PA > PD ...
... given distance from the foot of the normal . G. Of tracts drawn to points unequally distant from the foot of the normal , the one drawn to the remotest is the longest . Proof . In the △ PDA , angle PDA > PAD ( why ? ) ; hence PA > PD ...
Page 49
... is equivalent to another A having the sum of two of its angles equal to the smallest angle of the given △ . Data : ABC the A , a the least angle ( Fig . 40 ) . Proof . Through M , the mid - point of TH . XXVIII . ] 49 TRIANGLES .
... is equivalent to another A having the sum of two of its angles equal to the smallest angle of the given △ . Data : ABC the A , a the least angle ( Fig . 40 ) . Proof . Through M , the mid - point of TH . XXVIII . ] 49 TRIANGLES .
Other editions - View all
Common terms and phrases
adjacent angles altitudes angle AOB angles equal anti-parallelogram axal symmetry Axiom axis of symmetry bisect called central angle central symmetry centre of symmetry chord circle K circles touch circumcircle concur congruent construction conversely Corollary corresponding angles curve Data diagonals diameter dimensions distance draw a circle Draw a ray drawn Elementary Algebra ends equal angles falls figure film fixed point Geometry given angle given point given ray half-rays halves homœoidal included angle inner angles inner mid-rays innerly intercept intersection isosceles join kite Let the student locus medial meet mid-points normal opposite angles opposite sides outer angle pairs parallel parallelogram plane point equidistant point of touch polygon position Problem Proof proposition radii radius reciprocal regular n-side reversible rhombus right angle round angle secant Solution Space sphere-surface straight angle subtended surface symmetric tangent tangent-lengths Theorem unequal vertex vertices
Popular passages
Page 95 - A circle is a closed plane curve, all points of which are equidistant from a point within called the center.
Page 35 - Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal.
Page 43 - BDN, have the three sides of the one equal respectively to the three sides of the other...
Page 70 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.