The Elements of Euclid Explaind in a New But Most Easie Method Together With
The Elements of Euclid Explaind in a New But Most Easie Method Together With
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For if the Line touched * two Points of the Circumference, it would f be drawn from one of its Points to another : * and by confluence, according to this Pro* * pofition, would enter the Circle ; though, by * its Definition, the Line that touches ought * not to cut the Circumference. Theodofim \ t * makes ufe of the fame Pemonftration to c prove, that a Globe can touch a Plane only in ( one Point* for other wife the Plane would S snccjr within the Globe, E u M: PRC I Ho IE Nil The Third Boo\.
1...31 PROPOSITION III.
A Theorem.
If the Diameter divide a Line, which does not fafs through the Centre, into two equal farts, it will cut it at right Anghs ; and if it cut it at right Angles, it will divide it into two equal farts* IF the Diameter AC cut the Line B D, which does not / ;>afs thro* the Centre F, into j :wo equal Parts at the Point E, t t will cut it at right Angles. £ Draw the Lines FB and FD.
Demonstration. ' In the Triangles F E B and F ED, the Side E F s common ; the Sides BE and ED are equal ; Decaufe the Line B D is equally divided in E, md their B ifes F B and F D are equal : There- ire ( by the 8.
What to read after The Elements of Euclid Explaind in a New But Most Easie Method Together With?
You can find similar books in the "Read Also" column, or choose other free books by Claude Franois Milliet Dechales to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
For if the Line touched * two Points of the Circumference, it would f be drawn from one of its Points to another : * and by confluence, according to this Pro* * pofition, would enter the Circle ; though, by * its Definition, the Line that touches ought * not to cut the Circumference. Theodofim \ t * makes ufe of the fame Pemonftration to c prove, that a Globe can touch a Plane only in ( one Point* for other wife the Plane would S snccjr within the Globe, E u M: PRC I Ho IE Nil The Third Boo\.
1...31 PROPOSITION III.
A Theorem.
If the Diameter divide a Line, which does not fafs through the Centre, into two equal farts, it will cut it at right Anghs ; and if it cut it at right Angles, it will divide it into two equal farts* IF the Diameter AC cut the Line B D, which does not / ;>afs thro* the Centre F, into j :wo equal Parts at the Point E, t t will cut it at right Angles. £ Draw the Lines FB and FD.
Demonstration. ' In the Triangles F E B and F ED, the Side E F s common ; the Sides BE and ED are equal ; Decaufe the Line B D is equally divided in E, md their B ifes F B and F D are equal : There- ire ( by the 8.
What to read after The Elements of Euclid Explaind in a New But Most Easie Method Together With?
You can find similar books in the "Read Also" column, or choose other free books by Claude Franois Milliet Dechales to read onlineMoreLess
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