D E SCRI PTI V E GE O ME TRY FO R STUDENTS OF ENGINEERING B Y M YE E A B E R . B E . B A AM R O S . M J S OS . M , , , A ssistant P rof ess or of Mechani cal E ngi n eeri ng i n Charge of the Ill echa ni cal L abor a to r i es i n the Un i versi ty of IlI whigan; f ormerly I n str u ctor i n D escri pti ve G eo m etry i n Harvard Uni versi ty : E ngi n eer wi th th e Gen er al E lectri c Compa ny d W ti h K r a nd Co m an a n wi th es ng o us e, Ch u rch , e r p y Member of the A mer ica n Soci ety of M echani ca l E ngi n eers ; Jl I i tgli ed d es Ver ei n es deu tscher I ngen i eure; M ember of Fran kli n I nsti tu te; B oston A ss oci ati o n f or th e A d vanc e men t of Sci ence; A mer i can Soci ety of Ci vi l E n gi n eers ; So ci ety f or th e n etc P romoti on of E n gi neeri ng E du cati o , . T H I R D E D I T I O N TH I RD THOU S A ND NEW YO RK J OHN WILEY SONS ND O N : C M I I E LO HAP AN HALL , L M T D 1909 i h t 1904 and 1905 copyr g , B Y R J AMES AMBROSE MOYE PREFA CE . THI S book is the result Of teachi ng descri ptive geometry to n to n b S students o f engineeri g . My aim is prese t the su ject O as to make it most easily applicable to the requirements of recent n n i i n r n . n b engi ee i g practice The methods Of prese tatio th s ook , no t di n . n n therefore , are tra tio al Experie ce has show that most studen ts i n ou r best techni cal schools have difficulty in applying their knowledge o f this subject to subsequen t work in structural n n hi n b n n and machi e desig . Two t gs have ee attempted i this book to overcome thi s failure Of o ur studen ts : (1) The notation as in ni n F r is essen tially the same that used mecha cal drawi g . o n n and ri a lo g time , practical drafti g desc ptive geometry have had 2 to o little in common . ( ) The exercises have been carefully to n n i nk n fo r s and graded e courage a stude t to do th i g him elf ; , his n n n n to stimulate i terest , ma y co crete exercises , showi g usually b n n ns s . n practical applicatio , have ee i erted Such exercises , I thi k , be n b nni n so should i troduced from the egi g , that the student may n o f b n see the practical applicatio his pro lems as he goes alo g . The data for the exercises are stated by the system Of coor n n R dinates used i a alytic geometry . easons for choosing this _ F r b b . o i nn n hi b system are O vious a class eg i g t s su ject , there is a great advantage in stating the exercises wi th absolute defini te ni b is no t i n n . n n in ess If a defi te pro lem g ve , ma y stude ts , order i n to Show a sat sfactory solutio , will waste much time selecting data ; and others will present drawings that fo r their complication b are mostly unintelligi le . “ 2 3638 4 n use n r n Illustratio s are of more tha much wordy desc iptio . Fo r this reason an unusually large number of perspective and n n n l n in orthographic drawi gs have bee i serted . The i lustratio s n b perspective are very helpful . Whe ever it is possi le , however , studen ts should be en couraged to make models o f bardbo ard and “ n W n pe cils that they may build hat they are drawi g . - n L n This book is no t intended for self ins tructio . ike la guages , and this subject can be learn ed successfully only from a teacher , " n n b and s n o t alo e from ooks lecture . The stude t must take the n has b n o n time to work out ma y exercises . Space ee left the right n n and n ha d pages for lecture otes Sketches . The stude t may well n n o n put the solutio s for ma y of the exercises these pages . A f n to n b s 6 nd O 7 a 8 . good deal space is take explai Pro lem , , These are considered fundamental ; and the teacher Shoul d be sure " b n they are mastered efore the stude t goes further . With these b i n n be no w pro lems well mi d , there should difficulty ith those ‘ b n b n n that follow . It has ee my O ject to make the expla atio s Of the problems throughout the book consisten tly briefer as the b - s su ject matter i developed . n b n H and I am u der great O ligatio to Professor Ira N . ollis L w n n fo r n and n n Professor e is J . Joh so much assista ce e courageme t i n ri n b o w e n n prepa g this ook . I Special ack owledgme t , however , H n b n i n i . aco i b to Professor e ry S J y , who led teach g th s su ject l n He with its practical app icatio s . has carefully read much Of b and n n this ook , I have received ma y suggestio s from him . Fo r n i n n b assista ce ma y ways I wish to thank my rother, Mr . n f i a h B L o f . O i . J Clare ce Moyer, M E , Ph l delp a , Mr C . ewis n nn nd B n a . O f b Ci ci ati , Mr rya t White Cam ridge . A R Y . J . MO E C B RI G E D cem er 15 e 03. AM D , b , FA T T HE S ND D I P RE CE O ECO E TI ON. T HE gratifyi ng results with the first edition showed that the O f b b n n methods this ook were appreciated eyo d my expectatio s , n I n the second edition I have added a umber O f new exercises . Many O f these appear throughout the text . n n O f A I n r n . i . n prepa g the seco d editio the help Mr E Norto , F r b h B b n n b . o n P . and . , has ee i valua le to me valua le suggestio s n b n B n criticisms I am much i de ted to Comma der arto , U . S . Naval n n A s. K n A . n cademy ; Prof dams , Mas I st of Tech ology ; Prof e edy , n n n . H n . R n B arvard U iv . Prof Ogde , Cor ell U iv Prof a dall , rown f nn n n n n . O . n n U iv Prof Spa gler , U iv Pe sylva ia ; Prof Tilde , U iv . n Y n and . V Of Michiga ; Prof Tracy , ale U iv ; Mr W . Moses of n n the Ge eral Electric Compa y . l The American B ridge Company and the B oston B ridge “o rk s have kindly supplied drawings from which the data for some O f the n n exercises have bee take . ’ in Ferris s b I am much gratified that Prof . ook o n descriptive has b n b an ff geometry which just ee pu lished , e ort is show n to . i n e c n . in meet , a d gree , pra tical requireme ts S ce the first edi tion b n Of this ook appeared , I have received ma y letters regarding the . relative importan ce to be given this subject from a practical View n n n n n n n poi t i a course i e gi eeri g . These i quiri es in terest me much , and in i n I n i reply g have gladly give the results Of my exper en ce . A . Y J MO ER. B E n r 1 9 C RI G a u a 05 . AM D , J y , FA T THE H RD D PRE CE O T I E ITION. US RI n b n IND T AL educatio is ecomi g , every day , more important n n i i n all systems Of teaching .