Introductory Modern Geometry of Point, Ray, and Circle |
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Page 4
... , if the ceiling is not fourteen feet high , contra- dicting what is already said . In general , with respect to any position in Space it is necessary to know three independent All facts ( or data ) , and it is 4 GEOMETRY .
... , if the ceiling is not fourteen feet high , contra- dicting what is already said . In general , with respect to any position in Space it is necessary to know three independent All facts ( or data ) , and it is 4 GEOMETRY .
Page 5
... data , as of latitude and longitude , are necessary and sufficient to fix any position on it ; neither are more than two inde- pendent data possible ; all other knowledge about the posi- tion is involved in the knowledge of these two data ...
... data , as of latitude and longitude , are necessary and sufficient to fix any position on it ; neither are more than two inde- pendent data possible ; all other knowledge about the posi- tion is involved in the knowledge of these two data ...
Page 35
... data are : Two A , ABC and A'B'C ' , having the three equalities , AB = A'B ' , AC = A'C ' , a = a ' ( Fig . 27 ) . A A FIG . 27 . Proof . Fit the angle a on the angle ' ; this is possible , because the angles are equal and congruent ...
... data are : Two A , ABC and A'B'C ' , having the three equalities , AB = A'B ' , AC = A'C ' , a = a ' ( Fig . 27 ) . A A FIG . 27 . Proof . Fit the angle a on the angle ' ; this is possible , because the angles are equal and congruent ...
Page 36
... Data : Two ABC , A'B'C ' , having a = a ' , ß = ß ' , AB = A'B ' . Proof . Fit AB on A'B ' ; this is possible ( why ? ) . Then a will fit on a ' ( why ? ) , and ẞ on B ' ( why ? ) ; i.e. the ray AC will fit on A'C ' , and the ray BC on ...
... Data : Two ABC , A'B'C ' , having a = a ' , ß = ß ' , AB = A'B ' . Proof . Fit AB on A'B ' ; this is possible ( why ? ) . Then a will fit on a ' ( why ? ) , and ẞ on B ' ( why ? ) ; i.e. the ray AC will fit on A'C ' , and the ray BC on ...
Page 37
... Data : AB a tract , M its mid - point , Z the mid - normal , Pany point on it . = Proof . Compare the AAPM and BPM . We have AM = BM ( why ? ) . PM PM , X AMP = \ BMP ( why ? ) ; hence the △ are congruent ( why ? ) ; and PA = PB ...
... Data : AB a tract , M its mid - point , Z the mid - normal , Pany point on it . = Proof . Compare the AAPM and BPM . We have AM = BM ( why ? ) . PM PM , X AMP = \ BMP ( why ? ) ; hence the △ are congruent ( why ? ) ; and PA = PB ...
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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.